1) Are you sure you can't use a brake with your fork? You didn't provide any details, so I assume the answer is an absolute no. In case it is not though, there are solutions for difficult brake installations. Perhaps a Keirin brake might work, or a low-clearance brake? Perhaps not.

2) You might be able to run a rear brake if you don't mind the look of that?

3) While clipless is more secure than straps, both are more than adequate for brakeless riding. So, I wouldn't let this concern you largely ... the more important question would be, which system are you more comfortable riding with?

If your question is ... should you ride brakeless with the fork you want or braked with a less desirable fork ... that is a personal question. If you are comfortable riding brakeless, I see no reason from a safety perspective not to ride brakeless.

How important is the fork to you compared to your braking system? You'll have to answer that question, I suppose, but hopefully the info there helped a bit.