Ok, well remote-control-only is certainly easier than automated. You don't need an ASCOM driver, just something to turn off and on.
If you're really trying to keep it cheap, I think your only option is something homemade and motorized like the scope flap that Frank linked above. However, I've usually found that these kinds of projects, while fun, end up adding up to a lot more money than you think they should. :-). Unless you do a lot of DIY projects and have leftover materials and supplies, buying all the parts can end up nearly as expensive as buying something pre-made like a USB filter wheel.
As for on/off control of a device via wifi, there are lots of options. Amazon has a wide variety of smart plugs, which are AC outlets you can turn on or off from your phone. I use this one in my observatory, which is designed for outdoor temperatures:
If you want 12V control, you can use a Shelly 1 relay:
Note that these kinds of devices don't have a huge wifi range so they work better if they're close to your house's wifi signal, or if you have a router at your gear.