My father's got an old banjo that he needs re-stringed for him and I've got a set of guitar strings that I think would do the trick...But I'm not sure if these are appropriate for the instrument. I'm afraid I don't have any details on his instrument other than it's a banjo.
Guitar strings generally have a larger gauge, banjos use fewer wound strings, and scale lengths are different. As long as you keep the strings within the tension range the instrument was designed for, there shouldn't be any issues.
The big problem here is knowing the actual tension range the banjo was designed for, and finding guitar strings that fit that tension range. You'd need small gauge guitar strings, and wouldn't be able to use all wound strings. You can't just use any guitar string on any banjo, because of the gauge, tension, and wound differences, you can severely damage the instrument.
Because of this, using guitar strings on banjos is normally reserved for people who know what they are doing, in emergency conditions (you play with your band in 10 minutes and a string just broke), and as a temporary measure. Your case is even more delicate, since it's an old banjo.
In your specific scenario, avoid unnecessarily complicating everything and buy strings designed for your banjo. Keep it both simple and safe. As guitar and banjo players we are very lucky because strings are very affordable. Exploit this advantage, and keep it simple.
On my banjos there is one wound string, which comes at .022" Equivalent to a wound third on guitar. The others vary between .008" and .015" - all plain. So, yes, guitar strings will do, but you won't do it with a set, get individuals.
There may be a problem with the 'ball ends', although some banjos will be fine, and they'll fit, either between the teeth after the bridge, or over the pins on others.
Back in the '60s, we worked the opposite way, when banjo strings were used as lighter strings to make guitar playing and string bending easier. That was when there was only one set of guitar strings available!