There is a drawing/diagram of the C27 masthead in the "manuals" section in the Catalina owner's website.
www.catalina27.org You can't just order wider sheaves... the width of the masthead fitting is restrictive. The factory sheaves have a "U" shaped channel, rather than a "Vee" shape.... and can accommodate wire or rope. The problem is the rope diameter is limited to 1/4".... So... what to do...
Simple... build a "tapered" halyard.... where the high tech core, such as dyneema, is only covered where handling, cleating and winching are required. i.e the back half.
I have built a number of these type of halyards... and have described the process many times over the years. They work beautifully, run well through the sheaves, hold up well in the sun, and never produce meathooks.
On my boat I use an 80 foot core of 3/16 Samson Amsteel. The cover 40 feet of 5/16 Samson LS. The core of the inexpensive LS is used to fish the new high tech core into position. A "taper" splice buries the cover into the core at the transition point....approx. 1/2 the length of the total halyard. The covered 5/16 part of the halyard never goes through the masthead sheave..... So there is no need to climb the mast to change the sheaves out.....
The two splice needed are pretty simple. Instructions are on the Samson website.
If you have the original wire/rope halyard, there's a good chance that the two are NOT spliced together.... but rather the rope may be tied to thimble eye on the wire ... which means you'll need to pull off the exit block at the mast base... Whatever challenge you face in this area... the most important thing is to replace the old halyard with a messenger line...don't just pull it out...
A messenger line of thin cord can be spiraled around the wire and taped. There should be not heavy tugging, this slender connection should not get hung up on its trip through the sheave box and masthead fitting.
Use the messenger to run the new core....don't put the cover on yet... once the core is in place you can splice the eye into the shackle end... I recommend a large loop "luggage tag" size eye... this will allow you to attach or change the shackle easily.
Mark the taper point for the cover by attaching the messenger to the shackle and "hoist" the sail.... on my boat the cover is a few feet in front of the clutch... remember, you don't want the taper to reach the masthead sheave. Now you can bend on the cover.. tape the new core to the core of the cover line and start milking it through... following the splice instructions.
Note.. you can use 1/4" core, 3/8" cover... but.. it's over kill and way more expensive.
I found 3/16 amsteel on sale for less than $1/ft, the Samson LS was about .49 cents.ft .. so $100 for core and cover, and whatever you want to spend on a shackle.... much less than wire to rope replacement and a lot stronger.