Different Shipping Methods for different products/variation

I have a Woocommerce site. I have UPS and USPS plugins/calculators on the site. Right now, this means that whenever anyone purchases any product, they have the option between the two carriers. I would like to change that. I would like to have some of the products only have the UPS carrier option, and other products/variations only have USPS carrier option. Can this be done with Shipping Classes or another Woocommerce setting? Any suggestions?
Thank you.