Yes, you would want to strip it of all bearings for proper cleaning and repacking. Crank, steering head and both wheels. Bicycle mechanic skills would be required.
But here is another thing you can do: It is perfectly possible to change the gearing on your single-speed cruiser. The chain-ring on the crank can be replaced with a smaller one. And the sprocket on the rear wheel can be replaced with a slightly bigger one. A bicycle shop can fix you up, but you may be able to scavenge at least the smaller chain-ring from another bicycle.
Most cruisers have a one-piece crank, which is easier to disassemble than the three-piece crank on most mountain bikes. And with one-piece cranks, all chain-rings are interchangeable. You would need to change the length of the chain.
You could also buy a rear wheel -- or just the hub and have the wheel rebuilt on that hub -- with internal gears. These hubs are available with up to 15 gears (at extreme cost), but all you would need is the least expensive three-speed hub.
While I typed this, two other replies have appeared with similar information!