You can cut it just below the rim so it will fit back on itself. Use hinges that you may have to bend slightly in one or two places. Small heavy duty hinges about 1 inch may not need to be bent.
If you cut the top out inside the rim. you will have to screw a block of wood inside in about 4 places so the lid does not fall thru. Put an old cabinet pull or another small block of wood for the handle.
You can cut just half of the lid and hinge it in the middle if your watering can will fit.
We used a jigsaw to cut openings in ours.

I tried it cactus freaks way, and it doesn't seal up well.
Instead cut the TOP, inside the rim out. This leaves the upper lip intact on the barrel.
Cover the barrel with screening and secure with a good bungie.

GGG

Thats actually how my DH did mine.
But I don't like the whole top open. Even with screening I have to use Mosquitoes dunks. I have to anyway. They find their way down the gutter and down spouts.
I have not tried the way I sugguested.
Cutting does take about 1/4 inch away from the measurements.

GGG do you have a picture of yours? What do you hook the bungie cord to? I am not picturing this.