This Addon automates the process of collapsing down modifiers on a mesh with shapekeys while keeping the shapekeys intact.
Download the zipfile from the Releases page and install via Blenders Addon-Preferences
Edit > Preferences > Add-ons > Install... > Select SKkeeper.zip
This Addon adds 3 new operators which can be found in the 3DViews Object Menu:
Select the Object you want to apply modifiers to and select one of the options.
you can also search for the operators via the Quick Search floater (Hotkey: F3) and typing "shapekey" or other keywords in the names of the operators.