ANDR01DMy guess is that he's not planning to ski a whole ton of groomers if he's buying billygoats, though I hear they do ok due to the camber underfoot. If I remember correctly, they have a solid amount of tip and tail rocker (especially tip), so they will ski shorter than their length. You'll probably be just fine with the 186, OP.
assuming that you will immediately or very soon be a competent skier:
yes, that's a good size. that's a TINY bit taller than you are, and those skis have tip and tail rocker right? which means they will ski a little shorter than they would with no rocker
so unless youre going to have the skills of a novice, which i really doubt considering youre switching from snowboarding, yeah go for it
also billy goats arent park skis, right, theyre all mtn? which i will take to mean youre not a park rat and won't have any need for shorter than normal skis and will prefer stability