I have an extension cord that is 10 AWG and it is slightly larger than 1/2" in diameter.   The sheath and insulation is probably pretty think on a heavy duty cord like that.   You would probably have to use a 3/4" pipe if you want to run the cord through it. 

I don't think that you need to worry too much about weakening the pipe by cutting it.  all of the weight is probably supported at the ends near where it pivots so you could probably just have a few inches of pipe on each end acting as short axles and be fine.    You may have mentioned this but the way the Fischer enclosed the power strip inside the flip top is probably not a great idea.  If the breaker on it trips, you have to dismount your tool and remove one side of the top.  You really want access to the plug. 

As I mentioned before, I don't really find it to be an inconvenience to plug it in each time I use it.  If you don't want the cord dangling you can simply add a cleat to wrap each tool's cord around when you want to flip it over.  Because I didn't go the route of running the cord through the axle, I just used a steel stake instead of a pipe and I can simply use an unaltered extension cord to plug it in.   You could even add a cleat or hanger on the side of the cart to store the extension cord.   BTW,  The stakes were a little cheaper than iron rods (or pipe) and I think that they were a little beefier too.   

--Nathan, TX. Hire the lazy man. He may not do as much work but that's because he will find a better way.