Just about the thinnest necks you'll find are the old Ibanez RGs, late 80s/early 90s.
They started producing guitars with the classic ultra thin Wizard neck again recently, but they are quite overpriced IMO.
Personally I think those necks are simply too thin for long playing periods unless you have small hands, but ultimately the only way to know is to sit there and play for about 4 hours straight (with maybe a short break in between) and see if it's comfy or not.
There is of course, the normal Wizard I Prestige neck, 1mm thicker than the old school Wizard I necks. Same fretboard radius, different neck profile and IMO more comfy to play for extended periods of time.
Be warned the stock V7/V8 pickups are not amazing, but can changed out of course (Dimarzios Evos and D-Sonics work very well in basswood guitars like these)
The neck on my RG 7421 (7 string) is still relatively thin and flat, but I think it's something like 2mm thicker than a classic Wizard I neck. I can play this thing for hours and hours and most likely when I get a custom made RG-Style 7 string, I might ask to have the neck based off my RG 7421. The RG 7420/7421/7620/7621 have beautiful necks IMO, superbly playable and comfortable. I came from playing 6 strings for years, and my RG 7421 helped me get into the transition to 7s so easily, thanks to the neck.
The RG 7321 and RG 1527 have a similar sized neck in terms of dimensions on paper, but they feel vastly different to the 74/76xx necks. The 7321 is a lot more square neck profile wise and has a smaller fretboard radius lending itself (IMHO) to an overall slower neck feel compared to the bigger fretboard radius of the 74/76xx and 1527.
Not sure if the OP is interested in 7 strings, but I guess hopefully that will be of some interest to other readers.
Not quite as thin, but I absolutely adore the current Jackson necks that that are on the Pro series DK2 models (DK2S, DK2M, DK2). The thinnest necks Jackson have, but not Wizard I thin, but just super comfy and highly playable for the price.
I believe the only other model that shares that neck size is the Soloist SLS range.
The white finish one in particular IMO is an absolutely stunning instrument. The playability is just absurdly good.
Might be a bit out of your price range, but give it a go if you can find one.
I just make sure the action's low enough, and there aint no buzz. 
