The profile and shape of the neck are also important. Often taking a mm or two from the sides of the neck curvature will result in more change of feel than removing 2 mm from the overall thickness. Subtle refinements tend to make big tactile differences.
IF you are going to change the profile of your neck, you are the only person who can truly understand what you are searching for. Taking it to someone lese and declaring, "The neck is too thick. Please fix it...", can easily be overdone by someone else who can turn your 41 mm classic German profile into a telecaster neck. Then you just paid good money to $#@% up a functional neck!
It is not semiconductor physics; start with something like 220 grit sandpaper and give it a go. It is almost impossible to sand a neck too thin with 220 grit: Sand a little... play the bass for a week or so...sand a little bit more...play more...repeat. Once you get it to where you like, work the final sanding through 220>400>800>1200 to 0000 steel wool and then a bit of walnut oil.
The alternative would be to come by the shop the next time you are in Asheville. Bring those 4 pieces of sandpaper + steel wool and a tasty six pack of malted adult beverages or whatever else you need, as long as there is enough for two folks. By the time the sandpaper is trashed and there are six wounded soldiers laying on the floor, we'll have fixed your neck profile, played a bunch of tunes, and enjoyed a nice afternoon of laughter & storytelling while watching the chickens outrun the Redtail hawks, possums, and dogs around the garden in the big back yard park here at corporate headquarters...