I've been running 1/8" with a 3/32" chainring and a 1/8" cog on both of my bikes with no problems whatsoever.
As far as buying a new chain tool goes, I have a standard Shimano one that will handle either. I think most non-mini chaintools (not the wee Pedro one, for instance) will handle most 1/8" chains without issue. I was running one of those massive KMC freestyle chains with the taller sidewalls (is that what they're actually called...? I'm not really sure...) for a little while, and I had to go to the bike shop to borrow the $60 park pro chain tool to change anything, so that got ditched pretty quickly. But with a regular $10 Izumi chain you shouldn't have any problem using a regular ol' chain tool.
I can't see how mixing and matching between 1/8" and 3/32" widths will increase your chances of dropping a chain, but if there is a possibility, I'd like to know. I don't want to die.
m.