In order to remove the circuit board/etc, did you cut the black and white wires that feed into the light? I assumed you removed the unit from the ceiling and did the work on your bench. I am only going to using the switch.
Okay, I understand you better now.
You most definitely need to remove the fixture from the ceiling and do the LED conversion on your work bench. You will need to gut everything "florescent" and everything "electrical" related. You will remove every wire, the circuit board, and the sockets for the florescent tubes.
The conversion begins with only 4 reused parts as pictured below.
- 2 white pieces of plastic
- the lens
- the white switch
CLICK HERE to get to my detailed article.

Since you are NOT adding the night-light, your LED conversion will be extremely simple and most affordable.
As I mentioned before, I recommend disabling every-other LED circuit. Doing so provides the right amount of light, operates at only 3.3 watts, and also increases over-heating protection of the activated LEDs.
Be mindful that LEDs are polarized. If a light strip is dead, switch the wires around and it will then work. You will find it extremely helpful to have a DC transformer that outputs between 9V and 14V on your work bench to test things out when soldering and assembling. Any such transformer from a children's toy, small appliance, whatever, as long as it outputs 9V to 14V DC........not AC.
I advise to first convert only the fixture you use most. Install it and compare it to your other fixtures. That is what I did. I liked the results a lot so I committed to doing all 9 fixtures. I then removed the remaining 8 fixtures at the same time and operated like an assembly line doing the same process on all fixtures for easiest repeatability.
Like you, my childhood and early adult years were lean years. The lessons learned and creativity is in my blood even though I can afford today what others do. I'd rather do things myself rather than pay for expensive results that are often disappointing, most especially when other people are involved. There is a huge difference between a "professional" job done and doing it yourself. The pro is in a hurry to get out. Doing more myself also keeps me younger.