Can't do it. There are some things you can learn from the edge of the blade that get sloppy and take too long any other way. Also, especially in Western weapons, there are centuries of people working out very carefully efficient ways to kill and not be killed.
Maija (and Jake and Mac) got me thinking about this. What follows is a mix-- big things and little things. Don't waste time looking for a theme. And a caveat: I've trained and played with swords and other weapons extensively. I've even slaughtered livestock with swords... but I've never been in a sword fight. Take everything that follows with the appropriate amount of salt.
Margin of error:
Dealing with a sword, there really isn't a margin of error. Unarmed you can afford to make far more mistakes, give yourself more time. You take a glancing blow to the head or someone tags your upper arm with a fist and it's not a big deal. Bladed weapons force you to think in a more demanding way.
Weapons teach distancing faster and better than unarmed:
You need to be able, at a glance to tell from build, grip, foot position and weapon if the threat can reach you. Exactly how his range changes with shifts of footing, grip or center of gravity. You can predict the 'tells' you need to watch for when and if the threat decides to develop range. It's a critical skill with weapons and the cool thing is that it translates. After getting ranging with weapons down, unarmed range assessment is even easier.
You learn not to waste time or motion:
Related to 'no margin of error.' A sword fight is won or lost in fractions of seconds and fractions of inches. If the person is going to miss you by the tiniest of margins, you don't waste effort or time in motion. You never parry even an inch more than you absolutely have to. Unarmed fighting allows for a lot more slop.
It requires (and thus develops) commitment:
There's no way you can hit someone without being close enough to be hit back. Or maybe hit first. But we've all been hit enough to know it really isn't a big deal. With a blade? Any decisive action means you are close enough to be killed or maimed. Every time you engage you are betting your life on your skill, your speed and your ability to read what is truly happening.
This is specialized, maybe, but by truly limiting the weapon, strategy comes to the fore. Unarmed we can get by forever on tricks. Given just hand strikes, foot strikes, take-downs, locks, gouges, strangles, head-butts and slamming I can keep shifting between the options and force you to play catch-up, or find the one that you haven't experienced before. Limit it to just one class of tool (hand strikes in boxing, for instance) and it forces the skill to go up another level. t changes from tricks to tactics and then, maybe even strategy. Dealing with just a point (foil or epee) and limiting offense and defense to the same tool in the same hand pushed a deeper understanding of all the elements of strategy: timing and distancing and psychology and...
All of these things, and there are more, inform and improve your unarmed skill. They change the way you see and think.