I recognize the situation you describe and also dislike scented linnens.

On the other hand I do wear cologne every day and have rather a discerning nose. One of my absolute favourite hotels under the Hilton umbrella is the Conrad Hong Kong, and one of the highlights of returning there is the wonderful aroma which lightly permeates the entire hotel. It is not at all obtrusive (to me anyway) and gives me instant associations with Hong Kong and this property.

The perfume is Mandarin Tea by Shanghai Tang, the same as used in their bathroom amenity range. I have one or two bottles of the body lotion which I use sparingly whenever I want a kick.

Now if only the Embassy Suites in Bellevue, WA used the same one... but not on the linnens ...!