Confirming that changing the “Loading Behavior Override” property to “Force Inline” in the Sound Wave files fixed the delay. Tested in UE 5.1.1 in the editor and in a Shipping packaged build.
Tip: To change the setting for all your Sound Wave files at once without having to open and edit them all one at a time, first select them all in the Content Browser, then Right Click → Asset Actions → Bulk Edit via Property Matrix, select all the rows in the list and then on the right-side menu edit the property under the Loading category to modify them all. Then File->Save All