I don't know if the following instructions are helpful or not. -- They assume you are not going to reassemble.http://www.hp.com/hpinfo/globalcitizenship/environment/productdata/Countries/_MultiCountry/disassembly_monito_201032514049.pdf
It does seem to indicate the front bezel snaps on/off.
The illustration along with the instruction "Take out the OSD PCB" seems to show the on/off switch soldered to a small PCB. That confirms my thought that you may be best off to continue using the power strip as a switch. As to the effect of tuner cleaner on the screen, I would try to not get any on a plastic screen, which I assume it has. The power switch is below the screen. So you should be able to keep it off while getting some into the switch.
Or maybe you have this version: http://www.hp.com/hpinfo/globalcitizenship/environment/productdata/Countries/_MultiCountry/disassembly_monito_20112201827.pdf
which has the OSD PCB attached to the bezel. Same comments.
Looks like John found the same instructions.