To be honest I couldn’t find much out when I decided to research early one liners. It's true maxims - pithy sayings - have a long history but they aren't usually jokes. I managed to find this 1869 example from Mark Twain, and I think it squeaks in as a one-liner in the modern sense.
“I must have a prodigious quantity of mind; it takes me as much as a week to make it up.”
A little modernisation and Tim Vine could adopt that.
Mark Twain was famous for witticisms. Here’s a rather misanthropic one I came across, but it made me laugh.
“To create man was a fine and original idea but to add the sheep was a tautology.”
He didn’t care for President Theodore Roosevelt (eponym of the Teddy Bear) either. Listen to this.
“Mr. Roosevelt is the most formidable disaster that has befallen the country since the Civil War – but the vast mass of the nation loves him, is frantically fond of him, even idolizes him. This is the simple truth. It sounds like a libel upon the intelligence of the human race, but it isn’t; there isn’t any way to libel the intelligence of the human race.” (September 13, 1907)”.