As the thread has generally suggested, anything will do.
I'll accept for a moment the premise that you're valid in your desire to preserve and articulate your manliness via beverage choice. By the way, if you get dragged to a bar, you're going to hear the phrase "let's do shots" about ten seconds in, and your ruse will be dead unless you're desperate enough to chuck it over your shoulder. At any rate, little as what you drink and who judges you has to do with the size of your junk, I'm just going to table the ethics and decode the sterotypes as I understand them. I hang out with a lot of bartenders, so liquor culture is kind of my thing anyway.
Just order a normal beverage. Water, soda, whatever you'd drink anyway. Virgin cocktails are perceived as childish, but most of the other pitfalls in terms of classic girliness would actually have alcohol in them anyway. Ordering a Coke implies you want a Coke right now. Ordering a tequila sunrise implies that you don't want to harm your poor sensitive tastebuds with any icky liquor taste.
It also depends on what subculture you're in. We think of the frat-boy broseph demographic as one that carefully preserves an insular, masculine, honestly misogynistic culture, yet when you take away the tough drink names like "kamikaze" and "mind eraser," they basically drink "like girls." For the trendy club scenesters, anything vodka based is probably ok.
On a final note, you should really have mentioned where it is you're from and where these bars are. In Helsinki, I could walk in to a bar and order a Smirnoff Ice and probably not get any strange looks. Here in America I'd probably start getting hit on by strange men. In Dublin, anything other than straight whiskey or beer might provoke the same reaction (adios to my beloved Manhattans).