I'm not sure what plug type the ASIAIR needs but I bought eh Silicon cables from FLO like this:
https://www.firstlightoptics.com/astronomy-cables-leads-accessories/lynx-astro-silicone-power-cable-25mm-dc-jack.html
I bought the ones with the ring tongues, one dedicated to my AZ-EQ6 and then one with a 2.1mm end for my Pegasus powerbox.
When my kit was outside I put the whole shooting match, laptop and PSU in one of the plastic toybox type of box with a lid and no issues at all.
I probably wouldn't leave it outside naked, certainly not at this time of year anyway. It says it's designed for indoor use on the instructions but they all say that and 90% of astro folk with these will be leaving them outside in some way or other.