There is nothing to suggest that small spacecrafts can go to lightspeed in ANH or in ESB (I’m right, right?). Not once is an xwing (or other craft around that size) shown going to lightspeed in either of these two movies (although it is sort of implied in ESB). BUT of course ROTJ comes around and makes it clear that they can.

Seeing as how Adywans versions are not strictly bound by the PT or ST, I was going to suggest that Adywan could decide whether or not the smaller craft have hyperdrive or not.

But it was pointed out that in ESB Revisited they are indeed shown going to lightspeed leaving Hoth. So the whole thing is moot.