Before anything else, I too do not wish for things to get worse over in Ukraine, the whole situation there is ever so concerning. :/
That said, it would create uncertainty and that doesn't get along with risk appetites very well. So in theory it would cause people to run for safety to more secure asset classes (and historically that means the euro takes it a little on the chin.)
However: The biggest moves in asset prices caused by "war actions" and fighting were when it was unplanned and with little forewarning.
I can't tell you what will happen if Ukraine goes down that path, but I can compare it to other political/war turmoils we've had lately: Oil and Syria for example. As the threat of the US stepping in created uncertainty over the future of that region (and if the US will be sucked into another theater of battle,) the price of oil started creeping up in a very strong rally. It ran particularly strong when Kerry announced the US could start missile strikes in Syria in as early as a few weeks from his speech denouncing Assad... but once the first missile struck and US aid to rebels began, oil's run was over and we actually saw declining prices for a period of time. Why? Because the world had notice, it was planned, they had time to think out the risks and hedge, or not care since the impact on oil supply would be limited... The point was, it wasn't some snap decision and instant action that causes everyone to panic and be uncertain about the outcome (and by default, war in that region == higher oil.)
So how do we apply this to Ukraine? What will continued violence, or even civil war mean for that region and asset prices? Where will money flow? Remember, they aren't using the Euro, or the Russian Ruble.. so likely the Hryvnia will take more of a hit... Perhaps the Euro gets a little pressure too depending on how more more involved the Euro Union gets moving forward.
Really, I'm waiting on Russia to show their cards before I have a firmer opinion.. Politically speaking, this whole mess is extremely complicated.. and if Russia steps in to secure the pro-russian areas of Ukraine, that would make things rather messy.
Anyway, I can safely say I don't know enough about Ukraine's history, or every facet of the problems leading up to where we are now for that matter, to really contribute.. all I'm planning to do about it is follow along and watch Russia closely (not because of any distrust of them, just that I think the US and EU will be far more likely to remain passive for as long as possible in comparison.)