Edited Jul. 10, 2018 at 3:01 p.m.
Yeah it'll be very hard. Starting from there, let's assume Callahan and Johnson are both out of the picture (likely traded in the coming months or before the next draft). It gives them 27,25M$ to work with and 12 players to sign.
Let's assume Karlsson is in the line-up (via trade, which would just include prospects and picks), my bet is he'll get 9,5M$ AAV on a 8 year contract (the math says that he'll be getting 48 138 400$ in total cash after tax with that deal in Tampa, compared to 46 041 200$ in total cash after tax for an 8 year deal at 11,75M$ AAV in California and a bit less in Toronto). That brings the cap space down to 17,75M$.
Then, you have Point and Gourde to resign. I'm pretty confident in saying that Yzerman will take the same approach with Point than with Kucherov, so a 3 year "show me" bridge deal at around 4,5-4,75M$ AAV. That brings the cap space down to 13M$. If Gourde keeps the same level of play than last season, my guess is he'll have the same type of deal Alex Killorn got from the Bolts, which is a 6% of the cap hit on a 5 or 6 year deal, so basically 4,9M$ AAV for 5-6 years (considering the cap is at 83M$ next season). That brings the cap space down to 8,1M$ with 9 players left to sign...
So now what? You're missing 2 D-men (#5-6), a 3rd line winger, a complete 4th line and 3 depth players (one D-man and 2 depth F or 13th and 14th forward). That's the tricky part. You'll likely have hurt your youth to acquire Karlsson (missing Foote, Raddysh and maybe more), but you still have the likes of Katchouk, Masin and Mitchells that could step up...but they'll be in big trouble, that's for sure. I think if they go the Karlsson route, Killorn will need to be move next summer (in 2019).
One more thing, in ALL THOSE TRADES mentionned, in no way shape or form can they take back any kind of salary, unless it's a low paid fourth liner with little term left on his contract.