Do NOT try to strop it out. You will likely just put scratches in your brand new strop.

Seriously consider yourself lucky. When I was reading what happened, I was picturing an inch of your blade missing. Your damage is about as minimal as you could have hoped for. BTW, I never put my razor into the sink. I wipe the lather off with my fingers and then rinse my finger in the sink. I haven't dinged a finger yet!