I've never felt Jeeves to be any sort of malicious to Wooster, even though a lot of his schemes do end up with Bertie looking a bit of a tit. I think that's just Jeeves having a bit of fun.
But Blackadder outright hates his employers/friends and his only reason for using schemes to make them look stupid is because if he was obvious he'd get his head lopped off.
Atkinson can definitely pull off suave ("I'd forgotten how dishy you are!") but I wouldn't be satisfied if he played Jeeves anywhere near the way he plays Blackadder. Blackadder always has a hint of smarm, which just isn't Jeeves.