You can use any “seatime” that you have from any vessel, right down to your own very small boats.
I don’t remember the rules for these small licenses, but I think you only need 360 (8 hour) days for an “Inland” license. The schools that offer license Prep courses can help you with the application for free.
The small boat your on my have state registration numbers, and therefore no official "gross registered tonnage. " The USCG has some rule for estimating tonnage of state registered boats. If the vessel is “documented” with the USCG, the it will be “admeasured” and has an official “gross registered tonnage.” As a guess, I would expect a 35’ boat to be about 10 gross registered tons. You may only get a 25 ton license, but that’s a good start.