We have a similar problem at work right now, but due to different constraints we've settled on Base85. Slightly denser than Base64, but still just plain old printable ASCII characters and the following characters are still "free" so one can use them as field delimiters in a CSV-style format:
"',/[]\
Incidentally, this also makes them JSON-Safe.
Base94 uses all printable characters, and Base122 uses both printable characters and whitespace.
UUIDs encoded in various alphabets:
len algo value
24 Base64 padded wScmB8cVS/K05Wk+nORR8Q==
22 Base64 unpadded osnQ3DUDTDuUQBc9mBRYFw
20 Base85 rHoLuTk%W0fgpY+`c>xc
20 Base94 d(+H"Q/hP}i}d9<KeAt)%
18 Base122 @#FoALt`92vSt@
Base94 uses all printable characters, and Base122 uses both printable characters and whitespace.
UUIDs encoded in various alphabets: