darkSpyro

Apparently, there are 244 hats available to Skylanders now in Trap Team.

Does anyone know of a listing that includes all 244 hats?

Nope.
99 hats are from TT, the other 145 are from SF and the other previous games.
Depending on your system, if you have a [Select] Button, push that and it goes to your character that's on the portal. Click on [Outfit], followed by [Hats]. It doesn't list them, but merely shows their shadows. Once you get the hat, it will be revealed along with its stats. However, for the 145 hats from SF, you'd have load SF, put each hat on a Skylander, switch SF to TT, then load each figure onto the portal....and pray something doesn't happen.
I had my Roller Brawl crash, losing everything she gained, no longer able to read on the portal. Had to get a new one.

I think it's 245. That's the number on the 3DS Trap Team collection screen for hats. Don't know about a list though.

Here's some more info on hats. There were 147 hats in Swap Force (now known as Legacy Hats), so that means 98 new hats in Trap Team.

You can buy 36 of the Legacy Hats from Hatterson at the Skylanders Academy, but you need to scan in a Skylander wearing one of the other 111 Legacy Hats from Swap Force/Giants/Spyro's Adventure to enter them in Trap Team. The 111 Legacy Hats include the 4 special hats you could only get originally by scanning the Target Swap Force pre-order card (UFO Hat), Jolly Bumble Blast (Jolly Hat), Kickoff Countdown (Kickoff Hat) and Springtime Trigger Happy (Springtime Hat). You can scan those special figures/card to unlock them as well, just note that the Jolly/Kickoff/Springtime Hat are mixed up in Trap Team when you unlock them with the figures.