Drain Punch makes sense but don't, as you have said, replace HJK with it. I never used Mienshao like that before but a Darmanitan swept me once because I was planning to let it kill itself with recoil by Flare Blitz (it was scarfed) and as I believe it was my opponents last threat to me it would have been as easy end game for me. It instead just swept me with Fire Punch lol which I was definitely not expecting. Clearly if you are very Gligar and Flygon (HJK does plenty still) weak you want to use HP Ice on Mienshao but the fouth move doesn't really add much to Mienshao regardless.
I would stay away from Taunt though unless you have a real need for it since most SR setters might decide its not worth eating a HJK to the face to set up SR and they will just whop you with an OHKO after you Taunt.
Fake Out is extremely mediocre on Mienshao but more than once I lost to a Mienshao only because it had Fake Out so in my experience its not complete trash. I think however you should not be spamming it early game for "free damage" since its screaming for Cofagrigus to set up and sweep you. If you need a revenge killer just making Mienshao scarfed can be way more effective.
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