Pay attention to fast Olsen's comment.... Older boats that used wire to rope halyards often had smaller diameter sheaves up top... the thinner discs made it easier and more efficient to funnel multiple halyards through the fitting.... My Catalina 27 is a case in point. The groove diameter of the masthead sheaves is a smidge over 1/4 inch. I tried using a 1/4 sta set x .....but it was too small for clutches, not comfortable in hand..... and I HATE sta set X..... I can offer you a rant on that stuff, but I would be repeating myself and annoying the old timers here.
Anyway... the solution was to build "tapered" halyards.... where you put a cover on a dyneema core.. (or strip the cover from dyneema cored double braid, such as Samson Warpspeed.
For my boat I used 80 feet of 3/16 amsteel (stronger than wire, btw) as the core. Then I purchase 40 feet of 5/16 Samson LS... and used the it's Dacron core as a messenger to fish the amsteel into place. ON the Samson website, you will find the two very easy splices you need to finish the project, A
"tuck" or "bury" splice, where you bury the cover into the core to create the "taper".... and... a type II eyesplice for high tech single braid. I spliced the eye into the end of the dyneema while sitting on the fore deck after running the new halyard.. I recommend splicing a "luggage tag" eye .... it's just a large loop that allows you to easily bend your shackle on or off.
If you prefer a larger diameter line, the cover is 2/16 larger than the core. So a 3/8 inch cover would use a 1/4 core.... I wouldn't go larger than that...
Whatever you decide, check the size of your sheaves before you buy any line...if you find the need to replace with larger grooved sheaves... make sure they will fit the masthead casting. Good Luck.