I would not use synthetic oil in that engine unless you are certain the gaskets are all the same materials technology used after 1995. ( which I doubt). The materials technology used back then is questionable with regard to compatibility with syn oils. It might work fine but you could get leaking issues that are a PITA to repair and costly as well. If that bike isn't leaking your best sticking with conventional HD360 20w50. JMHO.
You can also use Bel-Ray 85w140 in the trans as that is dino as well.