Honestly, the Inquisitor if well built doesn't need much help.
Between 3/4 BAB, self buffs for attacks and damage, judgements, and bane the character will be a power house.
Divine Favor is a level 1 spell the player will be able to cast virtually all day (and with Fate's Favored) will add +2 to +4 to attack and damage. Divine Power when he finally gets it will continue to ramp up the power.
The only thing the player will really need is Double Bane, although this will burn through Bane quickly it will also deal an incredible amount of damage.
Overall, don't worry about your player. They'll be fine.
The reason why you've heard "this isn't terribly good" is because TWF isn't very good when you don't have many sources of bonus damage beyond strength. But the Inquisitor class is made of bonuses to attack and damage to negate the to hit penalties from TWF and is able to stack damage bonuses without a problem. Inquisitor are an exception to the normal statement.
The one thing your player may want to consider is Sanctified Slayer archetype which gets the bonus feats through the slayer talents and gets them studied target instead of Judgement, which is overall a pretty good trade for a TWf character.
Also, an Inquisitor should almost never take a domain and choose an Inquisition instead.
Just have your player read this.
If you did anything to help them, giving them free two-bladed sword proficiency is as far as I'd go.
Also, I want to advise you that letting everyone get the full benefits from the Skald while not taking the penalties is probably a bad idea. Skalds can buff nearly as much it terms of to hit and damage for attack and damage (for melee characters) and also provides a hp buff. At any time an individual can choose not to accept the raging song of the skald so they can use their spell casting and other skills.
When the skald begins a raging song and then on each ally's turn, if the ally can hear the raging song, that ally must decide whether to accept or refuse its effects. This is not an action. Unconscious allies automatically accept the song. If accepted, the raging song's effects on that ally last for that ally's turn or until the song ends, whichever comes first.
So each turn they can choose to accept the effects and gain the bonuses, or refuse it and choose to cast or do whatever else.
Basically your rule isn't really necessary.
I would recommend the Inquisitor to pick up Sanctified Slayer as an archetype. This grants him a pair of Combat Style feats he can use to get Improved TWF without having stupid DEX. In addition, sneak attack and studied target provide a stable source of damage that makes TWF a bit more worth it.
I'd probably advise him to build as this:
- Tactics Domain, provides a nice boost to initiative when needed and the 8th level ability allows him to grab a feat whenever he could use one as well.
- You could allow him to replace the weapon proficiency granted by his deity for proficiency with a two-bladed sword. If we wanna get technical, a good example is Achaekek. Achaekek has the War domain in its portfolio, which means an Inquisitor of Achaekek could technically get the Tactics Domain... and Achaekek grants proficiency with a sawtooth sabre, a weapon that can be TWF with no special penalties that deals 1d8 damage with a 19-20/2x critical multiplier. Those are exactly the same statistics and domain that this Inquisitor would have so as you can see, it's not really OP.
- For build, assuming Human on a 20 pt. buy:
1. TWF
3. Weapon Focus + Teamwork: Precise Strike
4. +1 DEX (Round it to 16 for max AC with a breastplate)
5. Double Bane
6. Teamwork: Outflank
7. Extended Bane
8. Slayer Talent > Combat Style Feat > TWF Style > Double Slice, +1 STR
NOTE: At 8th level, your dude can pick up a random feat through the Tactics Domain 8th level power for a number of rounds = his class level. This feat can be Power Attack, Dodge, Vital Strike, whatever he needs. At 8th level specifically though, I'd use it to pick it up Improved TWF.
9. Extra Slayer Talent > Combat Style Feat > TWF Style > Improved Two-Weapon Fighting + Teamwork: Paired Opportunists or Lookout
11. Extra Slayer Talent > Combat Style Feat > TWF Style > Two-Weapon Rend
12. Some teamwork feat, +1 STR
On 20 point buy, I'd build this guy like this with a Dual Talent Human:
S16+2 D15 C12 I10 W14+2 CH7
CON is the weakness here, but you really need 15 DEX to pick up TWF at 1st level. An alternative would be waiting until 8th level to pick it up with the Slayer Talent, since it ignores prerequisites.
Yet another alternative would be going less nuts with STR. Something like:
S14+2 D15 C14 I12 W14+2 CH7
That also gets you another nice skill point.
Since you mentioned you got a Skald though, that would give him a nice CON boost though.