This Blender Add-on is a replacement for the CTRL-TAB mode change menu in the 3D Viewport. It is invoked by CTRL-W (can be changed in preferences keymap).

The entire addon is in init.py.

Trivial operator that changes the active object's mode if it is different than the desired new mode

Trivial operator that invokes the menu that contains the buttons to invoke the change mode operator with different arguments.

The menu with entries for the modes. This tries to be a "smart" menu and only presents legitimate modes for the active object. It probably has some unintended omissions.

Type CTRL-W and select a new mode from the popup menu

To change the shortcut key, edit preferences and in the Keymap tab make sure that search mode is set to 'Name'. The easiest way to find the keymap entry is to type 'tla' and look for "Change Mode Menu". Open it and set the shortcut to whatever you want.