Militarily the smaller German powers might make up for the absence of the Austrians. Politically they certainly do not. In particular, I'd think the British, French (and maybe the Russians? I can't recall their attitude in OTL) would feel much more comfortable coming up with an arrangement and dictating to the Prussians and a motley assortment of lesser German states than to an Austro-Prussian alliance.
Russia is tied up with suppressing the Polish revolt, so won't be taking any particular attitude - certainly not to the point of fighting.
Napoleon III is busy chasing his will o' he wisp in Mexico, and Britain is keeping her powder dry for fear of getting entangled in the ACW and needing to defend the Canadian border. She might conceivably fight to preserve Danish independence, but not for a couple of duchies. At best, she might threaten war to uphold the 1852 Treaty, but that won't help the Danes much as they too have rejected it.
In any case, I don't really see how Austria could stay neutral in such a situation. It would be tantamount to handing leadership of Germany to the Prussians without a fight, and that is total ASB.