Ultimately it will depend on what the "converter" tool does, but generally they operate by either:
translating calls from one API to another (generally the OS API). The OS API for consoles is not generally public, so there are generally very few tools that could make such a conversion
embedding a runtime for the original language/technology into the executable along with the original version of the game as data for that runtime; this requires a runtime to be available for the target platform (the consoles), which is often not the case
Certainly it would be possible for you to port your game, but you will likely need to do more legwork than simply running it through a "converter." Unless such a path was already blazed for you, by other developers or the platform vendor, but that depends on the platform and your technology and the licensing agreements you have as a developer for the console.
The ".exe" file format in particular (Portable Executable) is fairly specific to Windows platforms.
The version of Downwell available on the Switch and the PlayStation platforms was likely re-built for the port to those platforms.