Clam-on track brakes.

Clamp, not clam. How do I edit the title?
Bought this a couple of months ago.
https://www.lfgss.com/conversations/268687/#comment12336381
Bought it minus the wheels, that is and stuck some cheap HOY 650 wheels on there. But I got it intending it to be my daughter's kind of cool street bike. It's really nice in the flesh and super-light. The trouble is (a trouble which I'd sort of anticipated) it won't take brakes.
My LBS guy says he can't/won't drill the front forks. I don't feel qualified to argue and I'd sort of rather not drill anyway.
So I was thinking about clamp ons. Can anyone tell by looking whether the bike is going to be too small, or the clearances too tight to take them?
It might not be apparent from the photo but the braze on the fork is right at the point where I'd anticipate the clamp might go. So that could be an issue. Would I be better getting a back brake?
The Dia Compes aren't cheap (£30 was the lowest) so it's not something I feel I can try and fail with.
Any help deeply appreciated.
Oh, and if the answers are all depressing, anyone want to buy a 48cm track bike?

Looks fine. Are the fork blades round section?

They're annoyingly in-between. Certainly not the thicker ovals of proper oval forks but not perfect circle round either.