I think you could just try following the labels as opposed to the color... ie. connect B to B, Y to Y and G to GH (that is high speed fan). See if it works but unlikely... I think you need a bit more in terms of wiring depending on what the coleman control board has in its design.
As for the "not needing 24v", that is basically true BUT, there are two reasons for the 24v part, one for operating the thermostat which the internal battery will provide and the other is to operate relays in the control system of the AC. If you don't provide some form of power either thru the thermostat (usually) or directly to the controller (then using thermostat to switch grounds), your controller in the AC won't work.
As other have suggested, you should try contacting coleman to get wiring information for the control board which will likely solve your issue.
This site might get you some info RVtechlibrary.com
