First, you are quite right, it's not "cut-'n-paste", but "copy-'n-paste".
And I'm afraid that PaintShop Pro is the only software that I have ever used (apart from MS-Paint that is), so I can't judge between all the various ones available, because I've nothing to compare them with.
But all you really need is something that can save in .pcx format. And I assume that "Lview Pro" CAN save images as .pcx, because you said that you managed to resize Harlan's reasources....so we are over that hurdle.
"Does PS have an easy 'selection tool'?":....well....sort of.
Dark Sheer likes the PS '
magic wand' tool, but I don't.
Like yourself, I prefer to use the 'dropper' tool to select the pink background, then the 'draw freehand' tool (to create what PS calls a 'floating image') to roughly draw around the area I want, and simply press Ctrl+T to use the PS 'Remove Selected Colour' tool. This shrinks the 'floating image' so that it includes every colour EXCEPT the background colour. Lastly, Ctrl+C copies it, and Ctrl+E pastes it, as many time as I want.
(Not knowing what Lview is capable of, may I suggest reading that link that I posted. Anything you don't recognise must be PaintShop only)
But you can do the same thing by drawing around the new hat, then pasting it on to the first frame of the Cavalryman, pink-out the bits you don't want, re-drawing around the new head (INCLUDING some pink background that used to have some Cavlarymans 'bits' in them that you don't want), then copy it and paste, paste, paste it onto all the other fames.
So the procedure is to get the first frame right, copy the head and shoulders with a bit of pink outline, and paste, paste, paste away. Job done.

And the same head-'n-shoulders can be used in ALL .flcs (with the exception of the death .flc, which is slighty more tricky).
Total time to do 500 frames with a new head.....1 or 2 days, thats all.
Once the hats are done, then just ask and Dark Sheer or I will tell you ways of changing the horse colour, should you wish to do so.
(But PaintShop Pro does have a lot of other quick features.
As Christmas is coming, may I suggest some subtle hints posted on the refrigerator?

)