We use our embouchure muscles for all kinds of things: facial expressions, speech, eating, kissing. Do any of those things “ruin” your embouchure? Of course not. The embouchure is made up of very flexible, agile muscles that are very capable of carrying out multiple tasks.
When people (almost always non-doublers) express concern about embouchure ruin, most of the time what they seem to be talking about is tension, or sensitivity loss, or buildup of callused tissue, or maybe strengthening the “wrong” muscles. If playing any woodwind instrument is giving you these kinds of problems, you are playing it wrong. Your embouchure for any and every woodwind instrument should be relaxed, balanced, and pain-free. Get some lessons with a qualified teacher, quickly.
Woodwind doubling presents real challenges. No need to invent fictional ones!