Throw the MRE TP away.
Get the real TP from your ruck, track or truck. If you did not bring enough real T to the field, you are an idiot and deserve to us MRE TP. Every vehicle usually had several rolls floating around it, somewhere, at a minimum. It was considered a necessary part of the vehicle, like engines or tires. For long field problems, several cases would be around. It was less important than water or ammo, but probably more important than fuel or coffee.
Wipe as normal.
Also, many places, especially overseas, everyone was so envornmentally sensitive, even ten years ago, that they did not want you crapping in cat holes. As a result, there was usually some kind of porta-john within walking distance. They usually got serviced every few days, including a re-stock of TP.