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md, it may be simplest to send a rigger aloft. They (or you) can climb the existing halyards using prussic knots, that's a standard rock climbing technique. And if the mast section has some taper to it, it is actually possible to climb the mast itself with prussic knots.
Or you can climb the line using ascenders (Jumar ascenders being the "name" brand) which are faster but cost more. The rigger will probably have them for jobs like this.
The catch in all cases is that you need to provide for safety, attaching to at least 2 lines or one line and one something else (mast, rig) to make sure that if a halyard comes undone, it won't drop you to the deck.
Unless you can get someone with a cherrypicker or bucket truck to raise you up long enough to untangle (or cut) the old lines and rig new ones. If you're not sure what will be up there and don't want to get new halyards yet, take some parachute cord and fishing weights aloft, and drop that as messenger lines for now.