Is there a device that can push down on a button with a wireless remote control?
Yes, this product. it pushes what you want using WIFI and application control:
https://www.switch-bot.com/?fbclid=IwAR2hdh84V8mSksl3F3-UPTUy3m94_0usT6hSwtfWXaob61n4ANCWSfBwnWo