It seems to me that this state will be less likely to expand a la the Nazis; it makes more sense for them to, in coordination with their business interests, say that they're building up as a "Bulwark against Bolshevism" and that they have every interest in being a power like any other. They will likely get away with remilitarizing the Rhineland and maybe Anschlussing as a bone towards the more ideologically nationalist factions, but won't have as much incentive to alienate everyone. On the flip side, Hitler's demands for a German ethnostate seem to me to have had a perverse logic towards France and Britain; while we now of course know that he couldn't be trusted that wasn't so obvious in '35-'39. Thus, the French and/or British might have more incentive to give the Germans a strongly worded "No", and conversely the Germans perhaps have more incentive to back down depending on who they need to please and whether they can do so while saving face.
The wild card for me is how the Soviets react, and how everyone else conter-reacts. Most likely I think that Britain is willing to tolerate rearmament but France isn't, leading to Franco-Soviet and Anglo-German blocs emerging. Given historical alliances, I think it's more likely that Japan joins the latter and China the former. Italy, I imagine, would remain neutral, as would the US.
Even then, since no power has an incentive to expand that can't be checked--the Germans by banking interests, the Soviets by the need for a French alliance, a cold war type situation seems more likely.