Can I just give it "bin\myapp.exe" and it will look under the base directory and find it?
No, it will start the app relative to wherever wyUpdate is started from (including the self-updated version of wyUpdate). In other words, you can't specify a relative path. You must pass in an absolute path.
Just form the absolute path either when your app is installed, or if you're calling wyUpdate from your app, simply form the absolute path before you call wyUpdate.