Cautery Swords are awful. Awful. As mentioned, a Nightblade is a better investment all around.

Glacius/Combuster have the same damage, so the question is whether you want the status effect to be useless in Fire strata (FSC!) or Ice strata. Note that Brandish status effects are only on charge attacks, and you'll typically be using those when you need to kite - I have a Blizzbrand and almost NEVER unequip it. You wouldn't use the charge on RJ anyway, but it can be very helpful when you need to stick a Lumber or Gun puppy in place while you deal with something else. Tick damage is better if you're often grouping with idiots who break your ice, but don't underestimate the icebreak damage - it's about half of the charge attack's damage and often kills things for me when I'm solo'ing (as in they literally come out of the ice effect and die).

Personally, I favor the Ice, but you won't go wrong with either of them.

Glacius or Voltech for elemental damage
Nightblade for shadow damage

If you have any kind of good anti-quicksilver weapon I'd go for shock. Chance for interupted attacks and good party friendlyness (teammates can't break shock like ice) are nice, but most importantly it's useful in FSC. Let's face it, pvp, merchants and a lot of other crown sinks/energy spending traps will have a higher priority than giving us more (varied) ways to earn crowns and become self sustaining.

We'll be stuck grinding our way to wealth in FSC for a long time. I hope I'll be proven wrong.

Just wondering, why would you consider a cautery sword and not a nightblade? Nightblade is sooo much better for slimes, especially since you can actually upgrade it. The only reason anyone would ever even get a cautery sword is cause they think it's upgradeable.