I would , and have upgraded several 13" trailers to 14" wheels using rims from a junk yard and tires from the used tire facility if using the trailer locally. If you are traveling away from home with the trailer I would suggest NEW tires and don't forget the spare. Or carry both 13" wheels/tires for spares and just change 'em both if you have an issue. Chances are when the flat tire fairy sees that you have 2 spares he will just pass you by.
2017 F350 Dually 6.7
He who dies with the most tools, wins!