Can I make shelf stable cocktail mixers by pressure canning?
I wouldn't pressure can most cocktail ingredients. The heat will ruin some of the aromatics of the ingredients (like how the citrus juices you get from the grocery store taste dead), and textures may change due to heating. 

Depending on how far the friend is, one thing you might want to do is freeze the cocktail mixes, then send them over packed in dry ice. Then, they shove the thing in the freezer when they get the package, and thaw it out when needed. 

Make sure to try freezing and thawing and preparing the cocktail before mailing it out.

Some cocktails will probably work better for this than others -- I suspect the cocktails designed to be made in big batches in Joy of Mixology by Gary Regan would be a good starting point. 

Also, note that shipping the cocktails sans alcohol is likely to be quite expensive if you're sending a reasonable quantity (in either the canned variety, where glass bottles are pretty heavy, or the frozen variety in which case you have to use a styrofoam cooler and maybe some freezer bags, freezing the cocktail in sheets and packing accordingly). 

Look at the costs involved, and you might find that buying your friend the tools necessary (if they don't have them), and sending a book of recipes may be a lot cheaper. You could also see if there is a grocery delivery service in the area which can send reasonable quantities of the required ingredients to your friend for a reasonable price. 

If you pick the right cocktails, you won't need too many ingredients to ship.