firstly, the toggle to enable or disable them should be next to where the search engines actually are so it's clear what the toggle affects

second, with the built-in search engines disabled, you should be allowed to use g, y, d, b, z, & w for custom site search shortcuts

third, you should be able to enable, disable, and change the shortcuts for the built-in search engines on a per-site basis like you can with custom site search. this one is probably the most work, but allows the most flexible customization