Wormy Chestnut for dulcimers - Clifford Glenn
Instruments- discuss specific features, luthiers, instrument problems & questions
Hey @kevin63, I'm no expert on friction tuners, but there are products called peg compound or peg dope that you might try. Since it appears you want to put on new strings (something we should all do more often), you might take off the existing strings first, then use a tiny bit of that stuff and work on the tuners before re-stringing. I'm sure others with more experience will chime in.
To determine string gauge, you need to know the vibrating string length (distance between nut and bridge). The age of the dulcimer really has nothing to do with it. Neither does whether you have ball end or loop end strings. You can use the Strothers String Gauge Calculator to get an estimate. That tool errs on the light side, but it seems like that's what you want to do anyway.
No tuning is necessarily tighter than any other, but some tunings may be tight for certain string gauges. What I mean is that whether you want to tune DAA or DAd (which would be the most obvious choices) will determine what gauge you choose for the melody string.
Since that dulcimer has no 6+ fret, it was probably tuned most of the time to DAA or CGG. So plug one of those tunings into the string gauge calculator, indicate the vibrating string length, and see what comes up. You will probably want to experiment and see what works best, but the calculator will give you a safe, light point to start with.