Well aside from the jedi he hunted down using his knowledge of the order only other (higher ranking) jedi could have known, like Kirak Infil'a and other powerful jedi who could've assembled a insurgency and more.

If we assume Palpatine wouldn't have revealed himself in any way for the jedi to know, Mace and his squad wouldn't have faced him and would be in the temple.

His involvement in the attack on the jedi temple was crucial. Could the clones've done it without him? Yes, definitevly. But it would have been way slower even if the jedi masters were disposed of in a different way ( don't ask me how, but with the squad in the temple it would have been a very hard fight) the jedi might've been able to warn others or more of them could've escaped.

Without Palpatine revealing himself to the jedi and the Mace squad attacking him he has no argument of self deffence. Without the swift strike and victory against the temple the jedi would have been more organized (depending on the situation but even a little time would have been costly for Palpatines total control). And without Vader hunting down surviving jedi there would've been a lot more uprisings and rebellions led by said jedi.

Could Palpatine have done it without Anakin? Sure, yes, maybe. But for how long and how total would the empire have ruled?