To expand on this:
An African king walked into a bar wearing a military hat.
Maybe this is Shaka (Zulu) wearing a PAC-Cap as shown here.
Only one third of his abs were trained –
One third of a six pack is a two pack (thanks to @Chris); so he’s a Two-PAC Shaka.
this was no Romeo.
So he’s a Capulet, which rearranges to El-Tupac (or Le Tupac, for the French).
The radio was playing Latin music without any mention of a sun god.
A famous Latin singer is Shakira, minus the Egyptian sun god Ra leaves Shaki.
His hands were trembling as he ordered his drink.
This means he was shaking, so he was a Shaker.
Putting it all together, he was an
El-Tupac Two-Pack Shaker Shaka listening to Shaki(ra)! (Say that five times fast!)
I agree that the most likely drink is @Chris’, that being
A Shot, based on his ultimate demise.