StreamOfTheSky
Adventurer
I'd allow it and in fact have actually allowed it in the past.
So have I. Of course, it helps when you'r actually following the rules as written, too:
http://www.d20srd.org/srd/skills/climb.htm
"You need both hands free to climb, but you may cling to a wall with one hand while you cast a spell or take some other action that requires only one hand."
Now, that's for someone even if they have no climb speed or sticky appendages at all. I don't care what the hell the spider climb spell text technically says, it makes no sense at all to ever say a creature can't fight with one hand while holding onto the wall with the other.