Hmmm... I don't know about the perlite - perhaps someone else can speak to that. I have microwaved soil-less mix without it before and really what you're going for is heat. I wet the mix (not sopping wet but damp) and put it in a pyrex bowl (easy enough to clean afterwards) and into the microwave. I zapped it on full power for 5 minutes, mixed it around, then 5 more minutes. It will be HOT HOT HOT so be careful.
Another option is to water with dilute hydrogen peroxide but that was unsuccessful for me.
The other, likely easier option, is to top with something like gnatnix or water with some gnatrol. I have done neither of these but perhaps one of these two ( @Ahead @Nysbadmk8
) can answer any questions you may have about that.