35A is the output of the converter; the current at the 120V input will be considerably less than that.
The basic solution is indeed to reconnect the converter with a switch or breaker dedicated to controlling it. Exactly how that might work depends some on what exact style of converter it is, whether you have extra space in your AC electric panel, and that sort of thing. One possible solution is to simply hook it up with a normal household light switch wired in to turn it on and off.
Depending on how old the converter is, it might be worth considering upgrading it to a modern multi-stage converter if you expect to be using it much.
