Can Lego Education WeDo 2.0 be controlled without using the app?
This is not possible currently using any of the hardware and software provided officially by TLG. However, there are several solutions that might work for you if you have a spare Arduino or Raspberry Pi around and are willing to do a little programming.
If you aren't aware, all of the Powered Up elements communicate via a Bluetooth protocol that TLG provides documentation for. There are several open source projects that make use of the API to interact with Powered Up devices.
If you have an Arduino available, you could try the Legoino project. This is capable of interacting with both Powered Up remotes and Powered Up hubs, so you can program it to interface between the two and provide remove control. Here's a video showing that setup in action controlling Boost:

If you have a Raspberry Pi or spare computer around, you might be more interested node-poweredup or pylgbst.