I did something similar when a built a new cart for my table saw last year. Used one of these:
And wired it up via Romex and surface-mount boxes both inside and outside the enclosed base. So now my table saw which ends up being another table in my garage during projects, is on wheels, has storage below, has two double outlets (one on front side, one on back), a double outlet inside, an idiot light, and a switch that turns some led puck lights in the storage cabinets below (which is why there is another outlet inside, plus that was where the table saw was originally going to plug in).
You obviously can't run a lot of high amp tools at once. But I'm comfortable running anything I would normally run over the heavy duty extension cord. Anyway. The wiring inside is left over 12/2 from another project, so I doubt it will ever be a problem.