Once you have the phaser selected I think you then have to click use on the phaser(once its next to the bag) and then click the bag and then on the welder. I haven't played the game in some time though.

Yeah, like the above post said. Taken from the manual - click the item key, click bag, click item. Item icon and bag icon will be in corner of screen now. Click bag again, and click 2nd item.

Not sure if this made a difference - But I had trouble the first time. Read the manual and tried again, and it worked - but I did one thing different. On the 2nd try, Before doing the above steps, I used the look function to look at the welder in the bag to identify it first. Maybe that had something to do with it?

I have the same problem it just won't do anything

Well this part took two hours to get past LOL

For those trying to do this - the phaser welder is NOT the thing looking like two phasers tied together. The phaser welder is the thing that looks like two little CO2 canisters with small tubes going around them.

Yeah it makes no sense but it helped sell hint books back in the day :)