Emphasis on "generally". Much of the weakness of your statement is in that single word.
Examples:
* East India Companies
* European 15th-17th century mercs.
* Japanese warrior monks.
* Boers
It's also difficult to use "irregular" in context of mixed opposition (VC/NVA, Mercs among soldiers in Iraq/AFG, Palestina campaign 1917).
By the way; what's a "regular" army and what not? That's another weak spot of your definition.
Some armies of the world include(d) militias and even partisans. The Russians would likely field many para-military, non-regular "army" troops in a future conflict (troops of ministry of interior, KGB successor troops, border patrol).
Germany gives combatant status to its border police (meant for WW3), while much of France's police is (para)military Gendarmerie. About 10% of the German Eastern front army in 1942-1945 were ex-Soviet troops ("Hilfswillige", people willing to help) who were employed with rudimentary markings and unarmed. They weren't officially subject to martial courts and such. Were these men irregulars?
What about Soviet Red Army troops who were overrun and turned to partisan warfare? Regulars or irregulars?
A 95% definition is no useful definition.
edit: I forgot to add Austrian-Hungarian border settlers, Russian Cossacks, letter of marque,
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