They wouldn't have to share them with an EU army, they could leave them for "national use" only and avoid any possibility of escalation.
Now the EU Army being a non-nuclear entity would make anyone using nuclear army against them "the villain" and onward one could easily justify using "all means" (there's stuff there I'd say even nastier than nuclear...) against them, so a "moral" deterrent could work fine in practice (since everyone knows you're technologically capable of developing the really nasty stuff if anything motivates you to...).
Which "stuff" is even nastier than nuclear? Chemical weapons aren't very effective against modern militaries. Biological weapons are nearly as dangerous to the user as to the target.
probably it's more like sharing "the COST of maintaining and upgrading it" :)) ...EU Army funds would probably be better spend on tech for urban/guerrila warfare + next gen UAVs, eg. stuff you'd actually end up using in a real war!
Heck Russia would probably have the military capability to actually win this war cleanly and quickly of they didn't have to invest billions in their strategic weapons that will (hopefully) never be used. If the current world leaders are competent, they are probably only pretending to properly maintain and upgrade strategic WMDs while covertly diverting the funds to other secret operations... If WMDs are actually used, we've all lost anyways, so it probably only makes sense to keep a huuuuuge stash of the cheapest + most destructive and suffering-maximizing stuff around (I imagine some hellish bio thing) for pure revenge end-game.
Now the EU Army being a non-nuclear entity would make anyone using nuclear army against them "the villain" and onward one could easily justify using "all means" (there's stuff there I'd say even nastier than nuclear...) against them, so a "moral" deterrent could work fine in practice (since everyone knows you're technologically capable of developing the really nasty stuff if anything motivates you to...).