I would far and away prefer to use a mechanical pump because of the simplicity of the system, but you have to use the correct mechanical pump. We have had a go-round on this forum lately with trying to find a mechanical pump that won't overpower the needle and seat. You don't want to use a pump that puts out so much pressure that you then need a pressure regulator, because I'm told that regulators don't work that well with an engine-driven mechanical pump. Simply start with a mechanical pump that delivers 5-6 psi and have it over with.
Here's an Edelbrock high volume pump that is factory set at 6 psi. I'd rather have 5, but 6 will probably work ok, particularly if you use a Holley carburetor. They'll tolerate 6 1/2 psi.
If you use the pump you have, make sure you install a tee at the carb inlet and run a line back to the firewall and up past the back of the hood to the cowl. Temporarily mount a mechanical fuel pressure gauge with duct tape or tie wraps or whatever on the cowl, so you can monitor the pressure delivered by the pump as you drive. This is the only way you will know definitively if you have the pressure under control or not.