This year might be tough. And the beginning of next year will also be. But then the flood gates open up. I am pretty sure you will see Kaprizov signed to an extension in less than 2 years. This year will be tight. But next year, the there are rumors that the cap is going to explode by over $4 mil. I don't know if it will go up that much, but I would say maybe $2 mil. That would give the Wild (as they sit today) a little over $28 mil in cap space for next season. And then the cap penalties drop significantly to about $1.6 for the next 4 years. That is nothing for today.
I do wish the Wild could just sign Gus for about $3.4mil for 3 years. Wallstedt should be on the roster by year 2. And if his is the second coming like a lot of "experts" are saying (I have seen much tape on him yet), it might make Gus an excellent trade asset for that 3rd year.
Either way, I really only see this season as being really handcuffed cap-wise for the roster. If players like Liam Ohgren and Marat Khusnutdinov land on the roster next year (reading that a lot of people think both will be NHL ready next season), then those contracts will be at a lower rate. That gives the Wild a possible chance to spend a little after this year.
Of course, it's all a crap shoot.