You can use centrifugal fans to reduce moisture so that mold will not form.
The primary purpose of the squeegee is to remove standing water, from the walls, glass, or shower floor (in that order), so that the water is pushed down the drain. Doing this will minimize the amount of water that needs to dry out, speeding the process, and minimizing conditions for mold. A secondary benefit is keeping the glass from forming water spots.
In lieu of a window or ventilation fan, toweling down the remaining moisture will provide more protection from mold formation, and it would be advisable to relocate the wet towels to a location where they can dry out; leaving them in the bathroom will increase the humidity in the bathroom, further delaying the shower from drying out.
Recommendations are to vent outside (not in attic) but sometimes that can be challenging. You might want to check your attic, to ensure it is adequately ventilated and that the moisture has a means to get outside otherwise you might be creating another problem area.
Panasonic makes very quiet ventilation fans; I have them in all bathrooms and toilet rooms. They also offer some with motion detectors as well as ones that sense moisture and will turn on / stay on until the moisture has reached an acceptable level. You can expect higher prices the quieter the fan and with each level of automation.
As for switches, I use these timers for the fans.
https://www.amazon.com/Leviton-LTB60-1LZ-Incandescent-Resistive-Inductive-10-20-30-60/dp/B00313JXB0/ref=asc_df_B00313JXB0/?tag=hyprod-20&linkCode=df0&hvadid=193989831776&hvpos=1o1&hvnetw=g&hvrand=10426584571972946088&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9029976&hvtargid=pla-318378259332&psc=1
Some additional information regarding bathroom moisture.
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