Nah, there's no such thing as an exercise that does what you're asking.

Ignoring the bullshit involved in gender norms, and ignoring the variances in different cultures, a cis man that went through male puberty isn't ever going to have the kind of body that would be considered feminine, on average, by exercise. Too much of what is considered feminine depends on boobs and hips. Boobs can't be exercised into existence, and you aren't going to change your skeleton enough to have the kind of hips that truly feminize a silhouette.

A cis man can definitely achieve androgynous looks, and can also shape their body to emphasize curves and such, but not by exercise.

Also, if your dick/balls are squishing, try different undies. You need better support, imo. My best friend is what you might call compact in frame, and is hung like a damn bull moose, but can do any exercise he wants because he has good support via well fitting undies. There's no single recommendation as per brand or style, but he's a briefs guy. I've worn boxer briefs for decades, and never had any issues when they were in good condition (though once they get a year or so of use, they loosen too much for comfort because the old frank n beans slide down the leg)