Conditionally Format Form Control Combo Box?

Is there a way to use conditional formatting on form control combo boxes? Suppose I have two rows for data entry with form control combo boxes (that's what you call drop downs, right?). Is there a way to make it so that if a user selects a value from one drop down, the other gets blacked out or locked or something visual happens to the non-selected dropdown so the user knows not to use both dropdowns but choose one or the other?

Furthermore, is there a way to do this without using macros?

Essentially I've got a client who will not let anything with macros run on its computers but we want the Excel file they use for data entry to present them with two drop downs but which are mutually exclusive (you only should select something from one of the two).

Furthermore, I know a solution using just data validation (use conditional formatting on the cells in a hidden tab that have the "source" options you can choose from), but a data validation drop down does not have other desired behavior (drop down arrow appears outside the cell, etc.).

So is there a way to conditionally format (or conditionally lock/protect/freeze) a form control combo box without using macros/VBA?

Thank you!