Why not use nylon guitar strings? I use steel guitar strings on my banjo. .010 (electric guitar light guage) for first and fifth strings, .013 (guitar medium) for my second string, .017 (guitar second) for my third and an UNWOUND HAWAIIAN GUITAR third (.026) for my 4th. Unwound strings don't go dead, the on on my banjo has been there at least 15 years and it still works.
you can get nylon monofilament fishing line in all kinds of guages. Using the foregoing as a guide, experiment until you find what you're looking for.
Joel Walker Sweeney, the inventor of the 5 string banjo was a classical guitarist and used classical guitar catgut strings on his banjo. Gut strings were still in use in the 1930's.