The story of the arming of Abyssinia involved gun-running on a massive scale.
The Abyssinians themselves kicked things of with a self-help project, capturing 12,000 or so Remingtons from the Egyptians in 1875-76 at Gungat and Gura (making the 500 Remingtons the Khedive had sent then-Ras Menilek to destabilize things look pretty meager). Then after the defeat of the Italians at Dogali in 1887, followed by the self-destruction of Yohannes against the Mahdists in 1889, most of the European powers were shipping modern weapons to the new Negus Negusti Menilek, despite the arms embargos in the Italian and Btritish ports at Massawa and Zeila, and despite German and Austrian prohibitions against export of weapons to Abyssinia.
The Tsar of All the Russias sent a personal envoy to deliver rifles and cash in 1891. Even the Italians supplied two million rounds (albeit of a different caliber than the rifles they had previously supplied) of rifle ammunition--just days befor Menilek repudiated his treaty with Italy in 1893. French and Russian advisors were training Menilek's army to use newly-supplied machine guns and Hotchkiss mountain guns just weeks before Adowa.
After Adowa, France initially offered 30,000 Gras rifles and a number of Lebel machine guns. They subsequently thought better of the machine guns, but provided 100,000 rifles and two million rounds of ammunition. And that only takes us up to 1897.
So Abyssinia (or more properly now, Ethiopia) had been well provided with a remarkable variety of arms even before 1900.
Allen
[Edited: too many typos!]