Pro-rated at the deadline, you'd get away with it. If it were made today, you're a tad over the cap.
As for next year, what does it matter? Everyone is signed.
MPS is in the AHL and isn't currently counting against the Blues cap.
Next year this move would leave us with ~$2.2 million in cap space with 19 players signed and Parayko needing a new contract.
That's not going to work, even if Parayko takes a bridge.
Still haven't addressed the problem of the Blues trading away their #3 center when they don't have an internal replacement available. Expanding the deal to include Klein and Berglund/Lehtera just makes it that much worse for the Blues.
If you want a Nash for Shattenkirk base, start by keeping those as the only two players involved and eating enough cap on Nash ($3.5M or more) to make the deal financially palatable for the Blues.
Considering that the Rangers made almost that exact offer already at the beginning of the season and the Blues declined it, it's probably still not enough.