I do not recommend using wheel barrow tires on these things. They are not designed for side loading such as what is experienced in a turn. Not to sound like a buzzkill, but you really don't want to be going 20mph in a turn and have your rim break.
Unless they are older wheel barrow rims, the new ones really are cheaply made. And the tires would probably peel off the rim in a turn. Sidewalls are real thin.