So, I'm not sure if it's actually the intention or something, but I wasn't able to go through the second level because I was killed when I was trying to reach the first arrow. The problem was that when I was leaving the cell without the spike, I was killed because the spike appeared on my cell before I moved to another one. If it is intentional, then I think it's a strange decision + I have no idea how to overcome this place since I need 2 steps to go through the cell without spike.
Also, I intuitively found the R restart button, but I might imagine some people being confused and not understanding how to restart. I think a little tutorial will be enough to fix the problem.
And last, the UI with arrows was kind of overlapping and it was hard to distinguish which arrow was already mine, and which wasn't. Maybe you might consider using different colors/opacities?
But overall, I think the concept is interesting for a very good puzzle. I wish I had the opportunity to play the game more and see how its puzzles go. But still, I liked it anyways, because out of all games with swapping controls, this one was one of the smartest. Keep up working on the game to make something good out of the idea!