I took the second layer off mine, it looks nicer to get down to the actual wood for sure, and I don't think it's too bad in terms of needing to come off because I got lazy on a log and there's streaks of second layer on it and the snakes have been fine! I'd make sure to get all the outer bark off though, and the second layer strips off easier if you soak the logs, I thought it would be easier to get off it it dried out, but nope!
Snakes climb over all sorts in the wild, a bit of bark probably won't harm them. We use cork logs in our vivs and they're covered in bark. We just make sure to boil and bleach everything we use.