It is not a bad idea, it does give you the effect of armor doing some work, but it does mean two different sets of rolling for soaking most every attack and could lead to some odd maths as it is giving more 'weight' to Body because you are using the full amount of body dice to counter both the stun AND the physical treating them effectively as separate actions.
Edited for new rollings:
So by your example you get to use your 4 Body to counter the 4 points of stun, thanks to the 4pts of armor, then roll your 4 body again to resist the 4 physical.
Law of average says rolling 4 dice should get 1 hit for certain with a chance of a second.
So they take 2-3 Stun and 2-3 Physical on average.
Compare that to the wet tissue paper as armor new rule where you only had 4 body dice to soak 8 physical damage, meaning they would have taken 6-7 physical.
So it spread out the damage as armor should.
On the surface it looks like its balanced, with the 4 pts of armor doing their job, but that might be because the armor and body happened to match.
Lets see what it does if Body was 6 and armor is still 4.
Same 8 damage coming in, but 4 get converted to stun.
Now we roll 6 body dice vs the 4 stun and 6 body dice vs the 4 remaining physical, effectively giving you 12 dice of 'Body' in all being rolled.
Law of average says 6 dice should get 2 hits, so they take 2 Stun and 2 Physical on average.
Again under the wet tissue paper as armor new rule, they would have been using the 6 body dice to soak 8 damage so they would be looking at 6 Physical damage on average.
Let's try this again for someone a bit more lightweight, Body 2 but same Armor Jacket with 4 Armor.
Same 8pt damage, 4 goes to stun and 4 stays as physical.
Resists each with just 2 Body dice, will be lucky if he scrapes off 1 hit each, so they are probably looking at 3-4 Stun and 3-4 Physical.
Which is not bad, considering using the new 'wet tissue paper worn armor system' they would have been sucking down 7-8 Physical damage.
They are still hurting, but it has spread the damage out.
So you are seeing double the amount of rolls used and will favour the High Body types thanks to splitting up the damage, though all Body dice will benefit from it of course.
Edit: I am growing to the idea, you are letting armor do its job after all, plus I LOVED my 3rd ed Troll who felt Light Ammo was a refreshing steel jacketed massage, BUT I think most will balk at having to do the extra splitting maths and extra rolling.
Personally we were suggesting a houserule where you just let worn armor DR add to the body dice, like it does for the Armor Spell or any cyber/bio bone augmentation, then you would be rolling 8 dice to resist 8 damage in your example. It has the benefit of being just one roll, but won't convert damage from P to S, so does lack in that regard.
In the end, it just depends on the level of granularity you want.
As for how to handle Pure stun attacks vs armor, that will take some thinking over.