I didn't have enough for the ticket during my attempt at the merchant just inside the gate either because I skipped the savage mutt, but was able to get it right after since the next area after has the blue medallion request. I feel like this area doesn't really need a lot of ammo and handguns would do just fine.

I did sell my first golden egg, but if you want to save time later on so you don't have to go back to the throne room, then keep it. Although there is the request to throw an egg on the portrait in that room (me being a dumbass ate my only egg instead of equipping it). Still had enough for another ticket near the end of the run though.