squeeze should be fine, even though it would be bottom end for me.
but if you squeeze it has to be way larger, 4x is my size if there are no coldcallers.
as played, I don't cbet the flop. multiway you want to bet strong draws and your valuehands. with TT we can't bluff on any outrun and have very limited chances to improve -> I would check

Playing this hand as a squeeze is a good way to go, your hand is pretty strong to be played only for its set mining value,saying that because its very hard to play TT multiway unless you flop a set or the rare low boards,and even then you have to be scared for overcards that will come very often.+ you dodge some heavy rake the times you win the pot.But as said above you really need to use a bigger sizing, you put yourself in a very tough situation where there might not be a clear answer for what you have to do next, CO range reactions to that sizing can be very wide but with no way for you to actually know what he is doing, for example he can bluff you wide worrying about the prize BU player is gonna get if he flats your squeeze, not wanting to play hands like AQ AK oop and multiway.On the other hand he can still be the nitreg who will only 4bet value, either way you wont have good context over what to do.If you go for lets say 3.80$ things are gonna be a bit more straighforward.And the flat flat scenario which is really bad for you its gonna happen way more rarely.Flop is fine you can get called by hands that enviroment does not bluff later like 66-99 and you deny 4 cards drawing equity like broadways with overcards, but even here the sizing plays a role, they might be having more things like AJo or TJs because of the small squeeze.Guys sizing is not to be taken lightly when you are into Poker. Preflop or on any street.