As said above, an orc would have no reason to keep the ring. They care not about power, only food and their own twisted fun.
It is true that Grishnakh tried to take the ring (which wasn't really there) from Pippin and Merry, but I don't believe he wanted it for power. Remember that both Sauron and Saruman wanted power. Ugluk served Saruman, Grishnakh served Sauron (I think). He wanted to show up Ugluk and return the Ring to Sauron, becoming more respected among orcs and uruk-hai and being rewarded by the Dark Lord.
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"What mortal feels not awe/Nor trembles at our name,
Hearing our fate-appointed power sublime/Fixed by the eternal law.
For old our office, and our fame,"
-Aeschylus, Song of the Furies
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