I agree about Morale Napoleon as an option. I have read the rules but not yet tried them, but they look interesting.
I use Field Commander Napoleon. A beautiful board game, covers all the time periods, designed from the ground up as a solo campaign game with a battle mechanism. The unit counters give you an OOB for your minis. There are numerous map boards to play the campaigns on for each period. Supplies matter as well.
The battle resolution mechanism kicks in when opposing forces are in the same area. I ditched this,instead set up my armies on my table based on the unit counters from the campaign board.
I use NeilThomas' Napoleonic Rules. They are fairly simple but historical and give a good game. And you can readily modify them to taste. But to this I add Nic Burt's Adjutant Introuvable. I think this is the best AI mechanism there is for horse and musket battles, and it should work with any rule set you are using.
This gives you the whole package, a great solo campaign game, and battles against a decent AI.
Last time I looked Adjutant Introuvable was a $6 USD download. Field Commander Napoleon comes with about nine map boards and a lot of unit counters. It's a Verssen game, high quality. Maybe around $$50-60.