I've never owned a Picnic Cat, but I'm always buying old boats sitting on old trailers, typically with old tires. If I'm going to tow it home any distance, I usually show up with new tires mounted on wheels, along with a jack and electric impact wrench, and almost always swap out the current tires/wheels for the new ones. Fairly cheap insurance. If you show up and the tires are nearly new and in great shape, then you can always return the new trailer tire/wheels, or keep 1 for a spare if the rig doesn't have one. Point is, unless the buyer says they are new tires, they are probably 5+ years old and due for replacement in the next couple of years anyway, why not do it before you start the long tow and be done with it?
When I bought a ComPac 23 (in South Carolina, towing back to MN) the owner actually agreed to bring the trailer over to a tire shop and get new tires put on before I showed up (I paid the shop by CC). That worked well too, I didn't want to bring 4 tires half way across the country.