Considering that ice fishing season is in full swing right now, I assume the OP has already bought something. However, I've done plenty of cooking and melting snow in ice fishing hub houses, so I'll share my thoughts.
I definitely agree that you want a liquid fuel stove for ice fishing. Propane can work just fine, but you'll have to stay on top of keeping the bottles warm. Canister gas is more fuss than it's worth, and you'll just be burning the propane from the mix anyway. You'll be able to start a white gas stove as soon as you get your shelter up, even if it's 15 below.
In a liquid fuel stove, if you're just melting snow and boiling water anything will work, but if you want to be able to actually simmer and cook (even something as simple as heating canned soup), you'll want a stove with control valves both at the pump and near the burner. Sure, you can kind of simmer with a Whisperlite (valve on pump only), but really not compared to what a Dragonfly will do (with 2 valves).
Apologies to the MSR fans, but frankly it isn't worth buying MSR liquid fuel stoves anymore. I've used Whisperlites and especially Dragonflies many times. They work fine, but most models haven't been updated in 30 years, and competitive models just offer more these days. The best thing going right now is the Primus OmniLite Ti. A 2 valve stove that will match anything a Dragonfly will do, but for about the same cost it weighs almost half as much, packs down to less than half the size, has a pump that won't break (unlike the plastic MSR pumps which I've seen break in the cold), and will burn not only all the fuels a Dragonfly or Whisperlite will burn, but also canister gas and with a simple adapter, 16 oz propane bottles. Further, the OmniLite is available with a screw-in, interchangeable silent burner that is superior to the 3D-printed silent burners you can buy aftermarket for other stoves. The silent burner alone would make it worth it over a roaring Dragonfly. For sure in an ice shanty you won't be talking to anyone with a Dragonfly running, but an OmniLite can be as quiet or quieter than a Whisperlite, especially at a nice low simmer.
One thing specific to running a white gas stove in an ice shelter is the fuel smell you get stuck with due to the cold and limited ventilation. While the stove is running it's fine, but priming and shut down are stinky. The best choice is a stove that doesn't require priming, like the old Coleman's or Soto's Muka or Storm Breaker (I have a Muka; it won't simmer, but I think a Storm Breaker will). These stoves start with a fuel/air mix instead of priming, so no plume of open flame inside your shelter, and almost no fuel smell. When you're done cooking, close the valve, set the stove out on the ice, and let it die there to keep the fuel smell outside. Unfortunately, all of these stoves have become hard to find.
My favorite stoves for ice fishing are the old Colman single burners with the tank at the bottom. I think the model 550B Peak 1 Multifuel is the best, but they've been discontinued for a long time. The model 533 Dual Fuel/Sportster II was available a lot more recently, should be easier to find, and should make an excellent ice fishing stove.