Just get the tom's skimmer and figure out how to hook it up to your existing filter, should only need a small bit of vinyl tube slipped over the intake pipe and the connector pipe from the toms.
It will be a fair pinch to fit it in a 10 but you can stick the lower end down in rocks if needed. Since betta are jumpers you'll want to put a cut plastic ring over the top peg.
That combined with a $10.00 walmart (marineland) aqua-tech shipping included would be under $30.00, if you've already got a 10g's filter it's a slam dunk.
F&S's bio cartridge is a sick joke too, supports HALF the bio equivalent to a UGF for the tank they're rated for.