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 apply_mods_sk.zip

This Addon adds 2 new commands which can be found in via the Quick Search floater (Hotkey: F3 or Space) and typing "Apply" or anything else in the names listed below:

• Utils: Apply Modifiers (Keep Shapekeys)
• Utils: Apply Subdivision (Keep Shapekeys)

Select the Object you want to apply modifiers to and select one of the options.