@maxdancona,
Think of cats. Some enjoy peoplized or even other cat interaction, some do not. Some are friendly with almost everybody, others are selective.
Same thing happens with other critters and yes, that includes humans.
People are not all the same. Some are outgoing, others just aren't. Some are touch-feely others don't want anybody pawing them.. For others, they are selective and hug, kiss or shoulder rub only certain folks and there are many who only want physical contact from people who they like. Not some random dude or dudette or even dudellette.
Want to shake hands down the road? No need to be asking. People can simply extend their hand it may be accepted...or not. Ask on hugs and kisses. Hugs up to now involve spreading arms wide in a welcoming pose and allowing a person to decide. Maybe keep that practice.
As to past handshakes, I am a left handed shaker. Doesn't bother me or most others. And yes, a person can use the left hand to shake the right hand of another.
You are too caught up in the current situation to see clearly and realize that this will evolve into something else. Yup. Same as life has always been.