I was also looking for an as slim-as-possible mechanical. I ended up ordering a Keycool 108 (I wanted full size) which, according to someone I found who has one and was willing to measure for me, is ~1.5 inches tall at it's highest point. That k810 you show is listed (on Amazon) as 1.3 inches, so not much slimmer.
The Maxkeyboards Nighthawks are also pretty slim. I think the specs on their website say they have a 1" height, but I'm not sure I completely believe that, i think that may be the case only, with the keys sticking up another 1/2 inch or so above.