Dyneema for furling line and halyard in old boat..

[Brion Toss]

Hello,
And welcome to the future. Which is like the past, but lighter. HM fibers behave like wire, in terms of stretch, but weigh a fraction as much, and are generally easier to splice.
But before we get to details about that, set aside any fears that traditional boats are inherently unsuited to these materials; as with any material, you can abuse/misuse it in ways that can harm your boat. The same could be said for a hammer, though, and we don't keep those away from classic vessels.
Classic boats are indeed more flexible than most modern ones, but most often, in my experience, that excuse comes up for boats that are tired, or badly-built. Applied correctly, any rigging material will only work with the loads that the boat itself generates. If the boat deforms excessively under those load, there is something wrong with the boat, not the rigging.
So, assuming you only tension enough to trim the sails correctly, HM makes a great halyard, much like wire, but better. And yes, you can make the working part skinny, and splice a fat, friendly Dacron tail onto it, just like wire (or sort of; the splice options are different).
Or you could use one of the "blend" HM's with only a portion of the core being high-strength material, and get a rope the same diameter as a Dacron one, but with half or less as much stretch.
There is little point in using HM for furler lines, as the loads are low, handling is paramount, and the cost/benefit just isn't there for HM.
Finally, if you look into Spectra standing rigging, you'll see that it takes much lower tuning loads than wire, precisely because it stretches so much less. This means it will be kinder to old hulls.
So yes, abuse is possible. You just have to learn how to use the tool correctly.
Fair leads,
Brion Toss