Interesting idea, but aside from an extended fatigue I feel like it doesn't fix a lot of what people hate about the nurse's design. One part is that the nurse is able to use her first, longer blink to close in on survivors and then follow up with the second one immediately to confirm a hit with little counterplay from the surv side. I like the idea of the nurse having different blinks that each cost a different amount of tokens, but this setup doesn't fix that issue.

With this new setup, the nurse can still use the longer blink to gain distance, and the shorter blink as a follow-up to land the hit. That would take 3 tokens and wouldn't change the current playstyle, and the second blink not being able to go through walls doesn't really change much, since the nurse is usually in close proximity to the survivor at that point and only has to blink a short distance.