Hi,
when you use kitty (beefed up putty) instead of plain putty, there is a "send script file" option in the menu. But this way isn't that good for real scripting, it just dumps the whole file as is. This can be a problem with commands that start a task (which you have to wait for before going on), or if you put some logic in your scripts. Error handling, loops, etc.
I prefer the ssh-cli for interactive working, but use a local installed cli for scripting.
But to be honest, I'm not a very savvy user of putty or kitty, so there might of course be a way to do better than I do