Since you are going to be taking levels in Alchemist to get the vestigial arms you may want to look at the Tinkerer archetype. When you take hands detachment your hand should gain the clockwork construct type/subtype. Alternatively you could dip a level into Clocksmith Wizard to get a similar ability to gain the clockwork construct type/subtype for your familiar hand.
I think Clocksmith wizard is a better option myself. I’m not too keen on having the hands normal stats overwritten with the Clockwork Spy’s stats but I figured I’d include it anyway. With the Wizard option familiar archetypes are more viable as you won’t lose them because of becoming an improved familiar like you would with Tinkerer. I think it would be funny but not practical to take Mauler for the hand and make it grow to medium size :)
One item I can think of to suggest is the magic item Arms of the Marilith. This would grant you an additional 4 clockwork arms that you can strap on. A generous GM might let you implant the arms rather than wear them. I guess you could get them made as a magic item tattoo and then the arms would be attached to you but that would add cost to an already pricey item. Also Clockwork Armor might be a cool addition but again a fairly pricey item.
Alternative to a clockwork hand you could get a removable clockwork eye by combining Eyebiter Mesmerist and Clocksmith Wizard. A cool addition to this would be to give it the Elemental Familiar archetype and choosing fire as the element. Then you could have your eye shoot fire at enemies (note that this should work even while attached as it functions as a tumor familiar and nothing in the text of tumor familiar prevents the tumor from taking actions while attached). It would also gain the ability to speak its elemental language.
No problem at all. I really like the idea of clockwork cyborgs in a fantasy setting. I wish Paizo had made a class that was based on that kind of thing.