Not sure you'll ever get enough pressure from an air pump to mimic the co2 system, certainly not enough to blast through that diffuser. Your best be is to get it going first, then check for leaks, etc.
Adhesives do not work well at all. Ive used everything from silicone, super glue, hot glue, various epoxies, water weld - nothing works for very long. Even if it seals off initially, they tend to break loose after you've taken the caps off a time or two. The simplest best way Ive found is this.
Push tubing through
Insert the connector, which expands the tubing in a tapered manner
Push it firmly back into the cap, hard, as far as it will go.
100% effective. No mess, no leaks.
Here's one of my set-ups. For the "adapter" I used a combination of check valves and air tubing connectors that come with those cheap discard-a-stone diffusers, like you see in the picture.
I have each line going in separately, that way I can see exactly what each bottle is doing. But you can pair them up just as easily and have only one going in and one going out.