Technomancer has several espionage themed spells and magic hacks. Check out the stuff from the first or second Threefold Conspiracy book, available at Archives of Nethys in the Sources > Adventures section. Plenty of CRB/COM stuff works, too, such as a cache to keep up polymorph all the time at level 6 as a permanent disguise.
The Street Rat Theme could also work great for a Spy. The knowledge from Street Rat seems very good for your campaign. You would be the ear to the ground especially in shady parts of the towns and spaceships.
Looking at the class skills both Biohacker and Technomancer have Sleight of Hand for hiding something to smuggle it through a checkpoint for example.
The idea of a Vanguard being a spy is nice.
Personally i like the Inversion Aspect for a Vanguard, looks very helpful for a group. Because moving enemies out of the way with reposition does potentially provoke an attack of opportunity or clears the way for your allies.
Bull Rush requires the right terrain but can be taken as a feat in addition to the free feat from the Vanguard Aspect.
The options you listed for your race both look perfect to be a spy!
For fly speed you can always buy an upgrade for your amour... I like the Astrazoan more because it's only a standard action to be someone else. I picturing a really quick change with a Astrazoan and a more difficult time to have a full minute as a Spathinae
For equipment a Spathinae would need the help of a character trained in Egineering or ranks in Engineering to adjust the armour or can't use the cool shapechanging ability!
In the end, take the race being more awesome in your eyes. They are similiar and both really cool aliens i would love to play.
Must have for every Technomancer if you ask me would be Magic Missile and if you want to survive nearly everything Life Bubble.
Token Spell to clean up anything on your clothes...
As for espionage spells... Mental Silence maybe?
You can also buy a computer and the module called Spell Chip to be able to cast certain spells from your computer which you dont' need that often to have them on your spells known list but often enough.
For special cases you can buy a spell gem. Because Spell Chips to quote a part of the rules for Spell Chips, they can be found on page 215 in the Core Rulebook, can be reloaded with the same spell.
And you would need to buy multiple Miniaturization upgrades for that computer so your computer can be a watch for example. Otherwise the bulk and size for that computer is high.
Spell chips cost 110% of a spell gem (page 224) with the same spells. When a spell is expended from a spell chip, the chip itself is not destroyed, and the spells can be reloaded into the spell chip for 90% of the normal price of a new spell chip.
Ideas for useful spells would be spells for Invisibilty or to see invisible things, to have different types of movement flying for example or Dispel Magic...
You should talk to the Mystic in your campaign some spells are also on the list for Mystics for Level 0 and Level 1 spells more likely then higher levels of spells.
There is also the Espionage Specialist archetype.
Most of the time, if you are just building a character without restrictions, an archetype is not a great choice - since the archetype is generally either lower power than what it replaces, or less flexible.
But for building a character with the restrictions of deliberately not choosing the best classes for that character concept, that is where an archetype shines. Giving some mechanics bite instead of just flavor.
Just to toss it out there, you could go soldier. Focusing on int dex cha in that order you can have tons of skills, feats for days (which could improve skills so much more or help you help your teammate), a full bab, heavy armor, every weapon available, and much more. I would also take the feat that makes you less susceptible to magic and play a race with bonuses to int dex cha. Could be fun!
There's also Special Ops training for soldier which gives you a nifty boost to some specific skills. It's enough to make you at least competitive with more skill focused classes. The Pistol Dancer fighting style or Aesthetic Warrior alternate class feature would probably be good fits
Bonus feats for Soldier need to be combat feats that's correct. But you still get the regualar feats for every uneven level.
How happy you would be with a class so few skills is up to you. Personally i like to have as many skills as possible but that's my preference as a player.
In the end many people just take one or two levels of Soldier most commonly the Blitz Fighting Style for more initiative and more land speed and to be profient in nearly all kinds of weapons and armour and shields.
Other Fighting Style with a great addition for your concept at first level is also possible.
With the theme for you campaign i would take a dip into Soldier for Ambusher for example. That Style requires to have Stealth as a class skill before you can pick it!
Street Rat does give you Stealth as a class skill. My Soldier for Society is a Street Rat. ;)
But you would really need a great initiative or being good as a group at creating a perfect ambush situation and you taking the first shot or throw or hit with a reach weapon.
I would look at what you friend is doing too. If they are going to be a skill monkey then soldier may be an even better option because it gives you the combat advantage. If they will not be as skilled then the soldier may be a poor option. But it is to taste too. If you two have a shared background you may have been the brawn to their brain.
Well, is the GM also limiting the rest of the build to CRB-only? That will also heavily limit the options for the other choices like Magic Hacks, Spells, and Equipment.
Also, Espionage Specialist is from Character Operations Manual, so that isn't CRB-only either.
Akashic Download/Tutor, Comprehend Languages, Disguise Self, Polymorph, Holographic Image, Hack Wetware are all good low level Technomancer spy spells.