I see the fork has disc brake caliper tabs. So yeah. You will need to replace the front hub with a disc brake hub (or the entire wheel).
As far as removing the coaster brake from the rear hub, not a good option. Taking the brake shoes out won't keep the clutch engaged. So a another rear hub that can take a single freewheel (or an entire wheel).
If you don't mind my asking what is the reason for not wanting the rear brake? I'm asking because you should be able to coast fine with a rear hub brake. If the goal is to stop better why not just add the front brake and leave the rear? It won't hurt anything to hit both. Just wondering.
I'm guessing you want to be able to pedal backwards as you ride. A niece of mine had me change her Dahon Boardwalk to freewheel for that reason. We added front and rear caliper brakes to that bike.
The coaster hub won't operate with the brake disabled. For a brake up front, it will need a new wheel set up for a disc brake, as mentioned above.
So, I would replace the rear wheel first, with a freewheel that has a brake.
Over here in Asia, band brakes are the easiest way to do that. A few of my bikes are set up that way. But band brakes don't work rolling backwards.
The rear brake is better than a front brake if you only have one brake. When turning, if you hit the front brake you can be thrown sideways and crash.