Orocarni dwarves always minded their own business in our halls deep beneath mountains, and whenever we had issue, we had to solve them on our own, without anyone's help. Therefore, we dont intend to invade Mordor, thats the issue of lesser races. Though we will keep a force in Khand to make sure, the orcs of Mordor dont enter our lands...
All the factions along the anduin, even the now independent force of orcs declared, that they will join together to face the darkness of Sauron and remove his presence once and for all. However while many set aside their differences for the greater cause the dwarves of Middle Earth decided to remain out of this "situation" and they will remain within their own borders. The mountains always protected them and right now, they don't see how sauron is a threat to anyone. The Dwarves of Erebor and the Orocarni dwarves remain proud and alone now, wishing nothing of the White council. One can hope, that while those that pledged to unite and defeat sauron, the dwarves remain on their lands and tend to their own.
"The Dragon is wise, a sage among the ignorant. He knows not all that glitters is gold."