Pipe insulation from the hardware store is cheaper and pre-slit. And will look equally, um, bad.

You can use cushy bar tape (try cork tape), double wrap your bars, wear padded gloves, change hand positions from time to time.

You can also raise the handlebar. If you ride >15 mph, you are giving yourself more work, since your aero drag is greater when you sit more upright.

You can also try sliding your saddle rearward. Why? Stand with your back to a wall, and lean your torso forward at the hips, you will fall forward unless you support yourself with your hands (on a chair for example). Now stand away from the walk, and lean your torso forward, while also pushing your butt backward. You don't need the hands as support, or at least not as much. Your core muscles are holding you in the torso forward/butt back position and that position is balanced.

Or, if your hands were fine before the time off, then you can just accept today's discomfort as the symptom of needing to work yourself back into shape. Maybe do some core exercises.