When a handshake is offered but your right hand is busy - such as while holding two beers or perhaps you're wearing a cast. Your only option is to shake with your left. If handled correctly, it comes off more as a low-five instead of an awkward hand-holding moment between two dudes.
When I turned, Dave had his hand out for a shake. He didn't see me holding my niece's hand, so I gave him a Southpaw Shake with my free one. No gayness.