Is it wrong to say excuse my left when giving someone an item with your left hand?

In modern Western Culture it is not an insult.

However, there are societies that do consider it insulting.

In heraldry the right (hand) is 'Dexter' and the left (hand) is 'Sinister', hence the expression a sinister person, it really means a left handed person, not someone who is 'underhanded'.

I am a sinister person, totally left handed. Casually and in fun I can be known as 'Cack - handed' or 'Gammy - handed'.

There are degrees of chirality (handedness) . I am 96% left handed. I might occasionally do something that is right-handed. Right- handers (dexter) will also have degrees of handedness, e.g kick a ball, or hold a bat etc.,

There is a web-site for left-handers.