How can I prevent "Open With..." from accessing external drives?

Frequently, when I try to open the (10.9) Finder's "Open With..." menu, I experience a delay that appears to be due to connected FireWire drives. This delay is very long when the drives need to spin up , but is also perceptible when the drives have not spun down. For me, this delay makes no sense: I have no applications that I use stored on my external drives, and I have disabled Spotlight searches of these drives (using Spotlight's "Privacy" setting ). Is there some way to prevent the "Open With..." menu examining external drives? --- Note that this is not a question about speeding up the OW menu in general (e.g., by pruning apps and file type associations), nor about keeping duplicate apps on external drives from appearing in the OW menu (I have none as my Spotlight settings noted above exclude them).