Two flannels, top and tail
Bits of an old flannelette sheet work fine. They wring out and fold down small. Dry off fairly quickly too if hung up to air.
Hard to beat wet wipes, but they're litter iimmc. That's not a criticism, just something that has to be bought and then disposed of.
Tengu, shops sell little packs the same size as paper hankies for handbags. Intended for schoolkids usually.
cheers,
Toddy