If you go with wood, it's better to find fin grain wood like bass, lime, apple, and dowels are not your friend.
Yards are tapered, and also have a number of faces and flats on them. Masts are also tapered, with even more faces and flats upon them.
Those tapers can be hard to achieve on die-drawn dowels, for the way the drawing process compresses the wood fibers.
It's actually mush simpler to take a square, and plane it to an octagon, then a "16th-agon" then "32nd-agon" and then to round than to plane flats on round dowel, then taper the dowels to need and suit.
You can make an appliance, by cuting/routing a 90º "V" in a block of wood and installing a screw or pin as a stop. Clamp the fixture to the bench, place the square stock in, and plane the top edge down to need. Rotate to work on the next edges. A router ot table saw will make the "V" cuts, you probably need 1/16"; 1/8"; and 1/4" deep cuts to handle Connie's spars.
Really, the plastic masts on the connie are good to the topmasts. The topgallants get skinny, and, you then run into the issue on whether or not the royal masts are stepped the way the kit has them. (Similar issue with whether there is a stepped flying jibboom over the standing jibboom.)
Unfortunately, I've managed to misplace my 'crib sheet' of the 6/8 sizes of line wanted for connie. Having eight "feels" very nautical for being rivet-counter precise, but the sizes can be hard to keep straight on the bench, let alone the rigging diagrams. Six sizes can be simpler, it being hard to discern the differences in 7, 8, & 9" circumference line at 1:96--and IIRC there's like 20, 22 different sizes of line "to spec" on a ship like Connie.
To your specific question, the rat lines probably ought to be visually 1/4 or smaller than the main shrouds. So, if you were using 0.08" shrouds (about 8" dia), you'd 'want' 0.02" ratlines. The ratlines should be a constant diameter for all the masts, even though the shrouds (might be) are smaller.
In some ways, this kit is tough on a rivet-counter. Details that matter, like the hull thickness at the gun ports, the shape of the gun carriages, the whole port lid controversy can get in a person's way of completing this kit. Change just one thing, and a body will start going, "Well, now I ought change [that other]" and you wind up with most of the sprues still left in the box <G>