I went out to the warehouse to take a look at the Ultra Faucets 6 Inch Drinking Faucet # 277-000189 referenced in your question. I measured a length from the base to the top of the spout of right at 6-1/4 inches. This should allow for a good fit without any interference between it and your window shutter.
I have attached an image with this dimension labeled that you can also check out. view full answer...
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