I don't know much about the Redding dies but I have both CH and Lee dies for swiss 7.5x55. One important key aspect is that you need to do with the swiss round is make sure that the sizing die REALLY sizes it completely. The k31 has a really tight chamber and a very short throat.
So you need to size the rounds down by making sure that you get the sizing down as low as the die can go while still allowing for a firm cam over.
Then you need to set the bullet OAL for your particular gun. The OAL listed in most books (like LEE) is set for the 1911 or other non-k31 rifle and is just too long. If you seat the bullets to the minimum OAL listed, you will end up with bullets that get slammed into the rifling and if you eject the round, it could yank the bullet out and dump powder all over the gun chamber.
Easiest way to check is to first set the gun on half safety. You pull the bolt ring out and turn it clockwise about 1/8th turn so that it sits on the bolt plate and is halfway between safe and fire. That takes the tension off the spring and allows you to still chamber the gun but with zero spring tension.
Then you seat your bullet (the k31 round works best with very very VERY little crimp or no crimp at all) and slowly chamber the round. If the bolt doesn't lock up very easily (just like you were locking it up with no round in the chamber), then you eject the round and seat the bullet a tiny bit more deeper.
Then you keep on slowly trying to chamber the round til you get to the OAL where the round chambers very easily with little to no resistance.
Another hint. After sizing the round and priming them, try to then chamber the sized brass with no bullets. You want to make sure that your sizing is done enough to allow the round to chamber properly. Once you get the sizing die set to as much sizing as it can and the empty shell then chambers fine, then go onto the powder filling and bullet seating stages.
I ran into a nightmare where I didn't check the sizing and kept on thinking that my rounds weren't chambering because of too much bullet lengh but in the end, it was just not being resized enough.
Lastly, this gun does NOT take well to neck sizing. Everything I have read says to not neck size the K31 round but make sure you do the full length size.
Good luck, it is a tough round to load for at first until you are aware of all the pitfalls that present themselves with the K31.