Bettas are carnivores and the few times I had shrimp (of any sort) with my bettas I wished I hadn't. Bettas are also curious and if they don't try to eat them, bettas often poke at the shrimp. Think it's probably stressful for the shrimp ;)
Also, as others mentioned, no matter WHICH type of shrimp, they're all very sensitive to water params. And the other reason they need a well established tank is so there's a good amount of biofilms and microscopic flora for them to eat. A betta might tolerate a minuscule spike in ammonia, nitrites, or nitrates...but a shrimp won't.
If you're eventually going to get an Edge and transfer your betta there, maybe just keep your current tank up and running, add more hidey plants, and put your shrimp in there (as long as it's gone through a whole cycle and established for a month or two). Then you'd have two cool tanks and everyone would be happy.
The more I think I know, the more I think I don't know much at all!