If you do choose to carry a cordelette, the first question is, what diameter, and how long?
For snow climbing or glacier travel, a good starting point might be 4 meters of 6 mm cord. For rock climbing, consider 6 or 7 meters of 7 mm cord.
On snow or lower angle alpine ice, you can build anchors usually pretty much wherever you want to, and usually the impact of a fall is going to be fairly low. Because of this, you can probably use a shorter, smaller diameter cord.
On rock, it’s the opposite. You’re going to have potentially higher impacts on the anchor, and your placements have to align with what the rock offers you and the gear you have left, which means they may be farther apart. Both of these point to using a longer, larger diameter cord.
Note that the strength increase going from 6 mm to 7 mm is pretty dramatic. 6 mm cord tests to about 7 kN (a kilonewton is a metric unit of force), while a 7 mm cord is about 13 kN. You only increase the cord diameter 1 mm, but the strength goes up by 7 Kn! For me, that’s a pretty compelling reason to use 7 mm cord for rock climbing.
Tie it “bunny ears” style, with a small figure 8 loop in each end, rather than the standard configuration of one big loop. Because tying it like this can give you a wider reach, you may find you can get away with a shorter cordelette. but try climbing on the slightly longer cord for a while and see what you like. (You can always cut off a meter if you think it’s too long, but you definitely cannot add one back on.)