Well, the tubes can handle the voltage. 

there are three issues, two of which you can adjust easy enough.

1.) Bias. Easy enough.

2.) Primary output transformer impedance.  You want it double for KT66's compared to EL34's. So, we adjust this at the secondary side.  If you are using a 8-ohm speaker load, you set the impedance selector on back to "4", if you are using a 16-ohm speaker load, you set the switch to "8".  A 4-ohm speaker load can no longer be made optimal.

3.) The problem is the KT66 likes a 470-ohm screen resistor, the EL34 likes a 1K-ohm.  You may not like the tone/performance of the KT66 with the stock 1K resistors.  If you swap out the resistors, you may not like the tone with EL34's.  Or, you can split the difference with a 820-ohm resistor, and and have more versatility, but not the best of either.

My advice...go with a EL34, KT77 or a real power beam 6CA7, which will all work great in the stock circuit, and pass on the KT66's.  People like to "roll" power tubes for tone, but the tonal impact of a power tube choice in an amp is maybe 2-3%, the big difference is how they break up closer to peak wattage.  Think about it, when was the last time you sat down with a record and could identify if someone was using EL34's, 6CA7's, 6550's, or 6L6GC's in their Marshall? I don't sit in an empty studio listening to an isolated amp, I hear it in a band mix where big changes have a big impact and minute ones blend into the background.  I choose my power tubes based on wattage dissipation.