I realized that since you can now give people things via the conversation menu, it is now possible to train by giving people training weapons and "sparring" with them. It is also possible to give your companions training weapons. The most reliable way to do this is to first trade them useless stuff (gems, socks, etc - anything works so long as it's not a container) for their weapon and pouch (and any other containers they might have). Then give them a training weapon. Having no where to put it, they will hold it in their hand, and will use it.
You can also take away the weapons and containers via wrestling, but then you have to get them to agree to end combat before giving them a training weapon. I think you may be able to get around this by starting a conversation, and then wrestling them, and then continuing to the "exchange items" option, but this might be a bug in the conversation interface.
I verified that this works a few different ways. I found a camp of wrestlers, stole their pouches, and then gave them training weapons and let them hit me for a long time. I also traded with all my companions to give them training weapons and then attacked a dwarf fortress I created, also all armed with training weapons. Everyone happily (and mostly harmlessly) beat on one another for quite some time. You do have to watch out for occasional injuries if people decide to punch/bite/scratch instead of using their weapons. You can prevent all injury to yourself (except maybe facial features?) by wearing armor, but I don't believe there is a way to equip armor on your companions and sparring partners without using dfhack (and the adv-bodyswap command doesn't seem to be working in 40.08-r2, but I might not have used it right). The biggest problem was my companions kept running off - possibly chasing after one of the dwarves who decided to run away after he was injured? You also have to watch that you (and your partners) don't get too tired, and take breaks when this happens (i.e. run away and come back later). The first guy I tried this on literally beat on me until he fell over from exhaustion, and then I left and came back and he did it again.
Not that there aren't enough ways to train your adventurer, but this one seems slightly less exploity than some.