Seldom mentioned solution to a very common issue.
Another option is to use a PERSONAL!!! sponge for backdoor maintanance.

I have this setup for emergencies (i.e. ran outta TP in the middle of nowhere).
Yes it uses water but it works. The sponge is kept in a sealable Tupperware container or similar and is kept clean and sanitized utilising PolarPure iodine solution so you don't have to use your drinking water persé.
When out on the trail for extended periods with no way to keep numerous rolls of TP handy, this works.
Of course I'll choose TP over this option anyday, but backups usualy save the day don't they.
Disgusting you say?
Having an emergency outlasting your TP stash and then have no alternatives... Now THAT'S disgusting!
Regards, Pharaoh.