That temperature will not hurt the eggs - I used a on/off on my first batch and it ranged from 87.5-91.5F all throughout the day. The babies hatched out very robust around 63 days later.

There is science out there that suggests temperature fluctuation can actually be beneficial to the developing embryo - atleast in sea turtles eggs. Of course this is a slow, consistent temperature change - not random spiking. Consistency is the key with incubation. You wouldn't want to have your clutch that's incubating at the same perfect temp to suddenly change half way through incubation, but a clutch incubated with the same fluctuation throughout is going to be fine. Just make sure your temps do not go over 91.5 for prolonged periods of time.

If you want to not worry about it I'd suggest going proportional (I chose a Herpstat for this year and I LOVE it!) but many people (including me!) have hatched eggs just fine with on/off style thermostats. Putting water bottles in the fridge should help with fluctuation regardless