Congrats on your yorkie!
When we got Luna the breeder gave her, her first bath the night before we took her home with us. I believe she was around 9 weeks old... Luna was fine and smelled great! I'm not sure if 7 1/2 weeks is too young though, but just letting you know when our yorkie had her first bath so you can compare... btw she is now 12 weeks old.
Also, if you just got him I would wait till at least a day or two so he can first get use to your family. But that's just me. We didn't give Luna a bath till a week and a 1/2 later... and the vet says we should only bathe her once a month unless she gets really really dirty.