Any tips for keeping glue off the veneer?
In this situation the pieces being glued together will already have a finish on them, so any squeeze out would just be wiped off with a damp rag. But if for example there was no finish, a trick you could do would be to glue the pieces, touch them together lightly, pull them apart, let them sit for a few minutes till the glue is not as runny, then put them back together, let them sit for another couple of minutes, then clamp.
You get much less squeeze out that way. Glue on a veneer is not the end of the world however. Not finding it before finishing is a problem. You can often find it by washing over the veneer with acetone, you'll see where it doesn't absorb. But getting rid of it isn't that big of a deal.
If you do happen to get some on the veneer, you're often better to just leave it there till it gets semi-hard, then peel it off, or scrape it off. A lot of people start on it right away with a damp rag and all that's doing is thinning it so that it gets down into the pores. Then it's a bigger problem.
An ounce of prevention, is worth a pound of cure.

Hope that answers your question.
Cheers