In impossible mode? Not sure how it is possible without magic spring. I think the real question is, why do you care to no loss this part? I assure you, later on it will be MUCH harder to no loss some battles.
Even if you do it with 'loss' you might find it isn't THAT easy either? (with soothsayer) <shrugs>, but at least you won't spend a lot of time waiting for web to expire and hope he doesn't chain web you.
I know that probably isn't the answer you want to hear. And I have done no loss in Armored Princess (killed Ktahu Impossible in 6 rounds no loss
), but honestly, I had a lot more fun once I got over the fact that I didn't have magic spring either as soothsayer and my build wasn't ideal for no lossing the spider.
If you insist, the problem is there is almost NO unit that can hit him without getting retaliated on and dying without sustained stoneskin.
One unit that CAN hit him is Jarl's Sweep attack IF you get a spider adjacent to the spider boss. But the gift spell might be expensive (never used it) and you don't have unlimited runes...
You can also try relying on transmute, but delaying in killing the spider minions is generally better unless you are doing a full blitz army for the reasons you said.