I know the title sounds ridiculous, but I will have to travel with about 8 fl oz of something like Play-Doh or Silly Putty in a couple of days.

It is for required therapy in recovering from a badly dislocated finger.

I am not sure how it would be classified. The nearest thing on the prohibited items page on tsa.gov is ...

Non-flammable liquid, gel, or aerosol paint

I don't think this is a gel, but you never know.

I don't know if I should pack in in my checked luggage or take it as part of my carry on. It is an organic compound and may trigger a false positive as an explosive.

Hopefully one of the DHS folks who hang out here or someone who has had to carry this kind of substance can offer advice.