I keep a package of those Adventure Medical Kits "Fresh Bath" wipes in my travel kit.

I typically have not been impressed at all with travel wipes and was skeptical of the AMK wipes. Based on AMKs reputation I decided that I would give them a try and I was actually very pleased with how well they worked.

In regards to shaving; I think NightHiker covered the bases pretty well.
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"There is not a man of us who does not at times need a helping hand to be stretched out to him, and then shame upon him who will not stretch out the helping hand to his brother." -Theodore Roosevelt