I'm sorry to hear about your grandfather. I bet he is getting a kick out of you diving into all the sailing stuff.
As I understand it, they went from rope to steel cable halyards many decades ago as a means for reducing the stretch in the halyard. It makes sense, since cable stretches significantly less than traditional ropes did. But in the last decade or so (others may be able to give you more specific timelines) newer, low stretch ropes have come on the market that are as good or better than cables, especially in this use case. Some lower stretch lines, like Sta-set, can work, but they will stretch a bit compared to the cable. For me, that's fine because I don't race and quite frankly I'm not good enough at the controls yet to really adjust the luff tension while I'm out. I'm more of a "set it and forget it" person when it comes to the halyard, unless conditions drastically change.
So, the natural question is, why bother to switch? To me, it's simplicity. If I want to make things really easy, I can tie a bowline, or a combination of a bowline and another knot, as the connection between the headsail and the halyard. Even if I wanted to use a metal connector of some sort, if that breaks or if the halyard chaffs through, I can simply cut the halyard a bit shorter and tie it off to the sail head. That's much easier than you'd have with a broken wire halyard. Plus, I don't like all the sharp ends on a wire halyard if/when it breaks. Granted, that doesn't happen often, but when it does it can be painful.
I also think that wire halyards tend to do more damage to the sheaves over time, causing them to need to be replaced more frequently than sheaves used with ropes. The rough-ish surface of the wire halyard tends to bite into the sheave, eventually wearing it down. At least that's my experience, although that mostly came from me having to replace the sheaves on our Catalina 3 winters ago, and not from long-term experience as a boat owner. But when there's something this simple that I can do which limits the number of times I'll need to go to the top of the mast, I tend to lean in that direction.
Anyway...if you don't want the stretch associated with something like Sta-Set, you can go with Dyneema or Amsteel. The disadvantage to those is the cost. For a 3/8" line, which would feel comfortable in your hand, the line can be a bit pricey, and it's really overkill as a halyard (the breaking strength would FAR exceed that of the cable it is replacing). Plus, Dyneema and Amsteel don't like to be knotted - they are a bit slippery - so the idea of "just" cutting off the end and tying a knot in it won't quite work, either. However, there are ways around this, including splicing the Dyneema/Amsteel to a length of more traditional line, this way you get the limited stretch for most of the halyard's length while still keeping the hand feel you want. Another is to use a "hybrid" line (my term) which has Dyneema/Amsteel at its core, but which has a jacket that makes it easier to hold. The end of the Amsteel/Dyneema can also be fairly easily spliced, if you need to make a repair.
All you really need to do is replace the wire halyard with an equivalent (or slightly longer) piece of an appropriate rope. You might want to inspect the sheaves, because if they are all torn up from the wire, they will eat your rope halyard.
If you aren't comfortable doing splicing, whipping, etc. (which is easier than you think if you haven't tried it), there are places that offer this as a service. We have a few riggers who regularly participate here, including index
. I've been pleased with the price, turn-around time, and quality of the work from him. I don't have any affiliation, just a happy customer. If you start a new thread about converting to rope halyards, he'll probably jump in.