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Mousing line? Is that the same as a messenger line?
I would use something fairly strong and inexpensive, like "parachute cord" to messenger the main halyards. There's no way it will break. If your local hardware store doesn't have it reasonably, you can us whatever cheap yellow polythene braided line they have--and if you need a floating line to throw or tow on the boat, reuse it for that. (Like the line to your horseshoe bouy.)
A couple of stitches with whipping line will ensure the end of the messenger line doesn't come free from the halyard, then a bit of tape over that to make sure it runs smoothly.
Depending on your fittings and any jacket on the line, if you're taking them down for cleaning you might also want to end-for-end the halyards. That is, reverse them so any wear on them is spread to different places. You'll get more life out of them that way.