Applying custom cape to badlion/lunar/laby mod

I had bought minecraft recently and I had used a cape and edited it, and I want to apply it to my skin.
This is the cape that I want to upload. I am fine with using any kind of launcher, the official mc launcher/badlion/lunar, but I want to apply it on my 1.8.9 as I play bedwars usually.

Any help would be appreciated, thanks in advance