Make White Shapes in Artwork Transparent- Knockout Group?

Hi everyone,

I've been struggling with making an icon that I'm needing to have trnsparent to be able to go onto both black and white surfaces. I did the artwork on a white background and just used white shapes to make gaps between my shapes to have them not overlap instead of forming the shapes around other shapes or learning about knockout groups beforehand(I know, rookie move). Basically, my artwork looks the way I want it to on a white surface but you can see there are white strokes and shapes that really form this into what it is which is ruining any chance on a dark background. Screenshots below:

I've spent quite some time searching on forums and youtube videos to see how I can turn these white shapes into transparent, lots say using the knockout group function is where to go but notyhing has worked for me. Is a knockout group even possible to solve this? I've tried to follow tutorials on that and it hasn't worked at all. The reason there is a wgite stroke around the hammer and the wrench is that after I made the shapes, I decided I wanted them both a little skinnier and used the stroke. Is there any way to keep the black shapes, or do I have to manually change the shapes after deleting this white stroke?

I tried to upload an ai file for reference but it's not letting me. I know I did some stuff in a janky way, I am new and learning... Any help is much appreciated!! Thank you.