Need Assistance with Immigration Ireland to Scotland

I am trying to figure something out. Due to
have more questions.

James H Connor married Margaret McMullen on 20 Oct 1857 in Hamilton,
Lanark, Scotland, before immigrating to the States around 1864. James
was born in Ireland, and Margaret in Scotland.

Margaret McMullen's father, Peter McMullen, married an unknown
McCloskie (McCloskey?). Peter was also from Ireland, and the unknown
McCloskie was also from Scotland.

Now, my working theory is that James immigrated due to the famine.

However, would there be anything such as passenger manifasts to try to
figure out when James and Peter immigrated to Scotland?

Ray...

There was and still is no immigration between
England-Scotland-Ireland-Wales, travel between these places is open and
free of any restrictions such as passports or papers needed.

Don Aitken...

And, although ships on these routes now have passenger lists, this is
a very recent innovation (since the Herald of Free Enterprise disaster
in the 1980s, I think). In the 19th century there would be none. You
just turned up and paid your money; nobody would be interested in who
you were.