Pretty much all weapon types are used by Orcs, If you want your Orc to represent a specific Clan I would try go by the Aesthetic of that clan in choosing my weapon:
Burning Blade > Sword, the runed sword from Hellfire Citadel is very fitting
Warsong > Axe, try getting the howling Warsong Axe or Gorehowl
Frostwolf > Axe or even Polearm, some not too “civilized” looking one
Blackrock > Axe (because you can’t use Warhammers as a Hunter), try getting one of the black metal axes
Bleeding Hollow > Axe or Polearm, one with stoneblade if you can find it
Dragonmaw > Polearm with Harpoon look, to catch and subjugate Rylaks/Dragons
laughing Skull > Primitive Stone Axes ,Polearms or swords. Make it look like the Wound would be more of a rip than a cut.
Pretty much anything works for Orcs, I’d say - in fact i’d say this for any race with a brain intelligent enough to know the pros and cons of every weapon. Heck, I am a huge supporter of Elves with hammers, axes or anything they aren’t romantically seen to be using. A hill I shall proudly die on.
But for your question, Ilayasha puts it right. Though any race should be able to use any weapon competently with enough skill, Orcish clans in particular favour certain weapons with a conventional legend surrounding axes such as from many of their heroic figures.
The Warsong for example use the Howling Axe, which is said to be notched with holes along the base of the blade (or on the blade?) itself to ring out a ‘howling cry’ that accompanies the clan’s tendency to sing mighty war chants during battle.
The Dragonmaw are well-known Dragonslayers and tamers that often use hooks and long reach weapons to bring down those wyverns that their home has many of.
Hell, even the Shattered Hand make good use of sharp tools to the point of ritually ripping their hands off and replacing it with a weapon. (Presumably to honour Kargath? Or the first time the Clan was made through the freedom of Ogre slavery.)