Well, you could thin it out with a thinned buttercream. I cannot see why a bit of milk wouldn't work, if you are worried about using it, just heat the Nutella up with a bit of cream or milk as suggested.
Usually milk added to something like this, when it is only a wee bit, will withstand being at room temperature for a couple of days because of the sugar etc. It is only when you use cups of it and it is the main ingredient, where you end up with problems.
Have you tried using it on its own? For filling a cake usually a thicker less runny filling is best anyway, Now don't forget to first make a stiff buttercream dam, but I cannot see why it wouldn't work well. Haven't bought it in a few years, but I remember it being of a thinner consistency. If you want it fluffier, add some buttercream icing or a chocolate buttercream icing to it, maybe about a third icing to two thirds Nutella. Another option would be to add some high-ratio shortening to it, this will make it quite a bit fluffier. Start by adding about 1/4 of high ratio shortening to the amount of Nutella and add more if needed.
As long as your room temperature is below 75F and it isn't sitting in the sun, you won't have any problems with adding a wee bit of milk or cream.
I hope that the guests will be warned of the use as many, many people have a severe reaction to nuts, particularly peanuts, almonds and hazlenuts (filberts).
Hugs Squirrelly Cakes