To safely train weapon skills one really should first train the defensive skills; armor user, shield user, dodging, and observer. This of course requires armor and a shield; these days it's easiest to just start with them. Observer can be slow to train, so I usually start with several levels and a few levels of the others and which ever weapon skill.
Then it's a matter of finding some one with their own weapon to train with; but you don't want them to be more skilled or much larger than you. Goblins do nicely. Once you've found them, there's two ways to train weapon skills.
First is by parrying their attacks in the Aim an attack menu; this will train the the skill used for the weapon used to parry, while minimizing the odds of taking damage. After you parry each attack, wait with . until the A menu shows another attack coming. Using . (period) to pass time seems to stop as soon as you can observe an attack is incoming; there's also , (comma) to only pass one tick if you want to be certain, but that will take a few presses.
Second is by using the multi-attack system available when Aiming an attack, doing as many attacks as possible makes each attack weaker and thus less likely to kill your sparring partner. But this runs the risk of taking damage, especially if their weapon skill is better than your defensive skills.
Or you could make a wooden training weapon with the limited crafting currently available and use that to avoid killing them, but that limits you to the sword, spear, and axe skills. You might even make two and giv one to your victimsparring partner, but these days they'll probably just try to run away if they aren't already military trained.
Now, there are a few ways to gain a combat advantage over an opponent. A prone opponent suffers combat penalties, so you can try to make it so they can't stand any more. A nauseous opponent too, so you can try attacks to their lower body. Finally, a winded opponent, by attacking the upper body, but that lead to them suffocating.
There are other ways, of course, but some of them are exploity and therefor not best, and there's training in fort mode but you already declined that option.