I have no real words of wisdom, but if it were my puppy, I'd probably not worry about it much, but just leash walk down the stairs.
If you don't have much other option, you don't have much other option. Plus, in my honest opinion, it'd be better for the puppy to walk down the stairs a few times a day with the (probably very slim) chance of it somehow affecting his physical health later down the road than for you to attempt to carry the puppy, which could either result in a nice fall down the stairs or otherwise hurting yourself in some way.