I think Phil has offered up some good advice should you decide to try & make a repair & find that the split can be closed up without excessive force. Everyone has to start somewhere & if it's your first attempt at a repair it can seem a bit daunting & you might have the worry of things not turning out how you hope.
I've had to repair splits in things once in a while, squared edged things can take clamps well & faces can be protected with scrap wood but for awkward, rounded shapes I tend to avoid clamps like f or g types & instead use a tourniquet or series of tourniquets made out of strong webbing. They are forgiving in as much as they are kinder to the surface of the wood & they don't slip if you do it properly. However you can glue them to the surface if you are not careful, so cling film between the wood & the tourniquet. Use glue/ adhesive sparingly, enough to do the job, but as little as possible to avoid unnecessary cleaning.

It's doable if the split closes up but if it doesn't then your not much further forward. Maybe leave it for a bit & have a think, maybe even induce a split in an old tool handle, like a chisel or hammer etc & try repairing it to have a practice. Might be worth a practice to see how that goes, gives you a dress rehearsal for the main event should you decide to go down that route soon or even later if you are happy to leave it for a while. It's over 100 years old so maybe there's no need to rush anything if it's not getting worse.