Auto-populate cell if data validation list has only one option

Hi all,
I have a series of drop-down lists created via data validation which pull from a separate sheet of dynamic lists that are driven by a series of rules. In other words, my sheet consists of a series of conditional drop-down lists, each one affecting the available options in the lists that come after it.

In order to best explain my issue I am going to describe two scenarios.
Lets say the first drop-down list allows the user to select from a series of hardware types (cabinet knobs, drawer pulls, robe hooks, etc.). The next drop-down lists allows the user to select from a list of hardware mounting options (through-bolted, surface-mounted, or back-to-back).

Scenario 1:
The user selects drawer pulls from the first drop-down list. The second drop-down allows the user to select either through-bolted, surface-mounted, or back-to-back as an option.
Scenario 1.jpg

Scenario 2:
The user selects cabinet knobs for the first drop-down list. In this case the second drop-down list only allows them to select through-bolted as an option since the hardware company only sells through-bolted cabinet knobs.
Scenario 2.jpg

Example.xlsx

My dilemma is this: I want to retain the ability for the user to select either through-bolted, surface-mounted, or back-to-back in the first scenario, but at the same time I want this same cell to be automatically populated with "through-bolted" given the second scenario so that the user does not have to go through the action of selecting "through-bolted" from a list that has only one option anyway. There are many scenarios where a proceeding drop-down list will end up having only one option based on what was selected for preceding drop-down lists and I want to make the number of button clicks necessary for the user as low as possible.

Any ideas or is this even possible?

Thanks,
Jack