Don't worry about it too much. CMYK is 100% going to look off once you view it outside of something like clip studio or photoshop. CMYK is intended for printing since it matches the colors used by the ink cartridges of your printer (cyan, magenta, yellow, black). It generally results in darker colors since mixing all colors produces black. Your monitor is using RGB (reg, green, blue). This produces lighter colors since mixing all colors produces white. We use CMYK mode in our art programs so we can see what something will look like when it prints. But you have to view it in photoshop or csp to see it. Other programs will not be smart enough to handle this - case in point. If you pass it off to a browser for ex, it doesn't really care about this and just assumes its RGB and renders it weird.
EDIT: If you have access to photoshop, it does a very good job of converting between color profiles.You can do it under edit-> convert to profile. Also, don't save your CMYK image as PNG. Use a jpeg at max quality. PNG is intended for RGB.
EDIT 2: Can you link me to that converter? I just had a hunch,