But why would a person who had probably spent his entire life (or very close to it) training with the bow suddenly decide to give it up and become a swords-master? After all, they originally chose the path they took, as opposed to becoming warriors, which they could have. Some Flavor texts from M2 support this:
" ... on occasion an archer of promise is sent to the Ermine, the homeland of the fir'Bolg, to study his craft at one of the three war colleges: jo'Za-Thatal, wa'Ama-Tchal, or ai'Kijin-Tak."
-Bowman Flavor Text, Myth II
And especially this one...
"When asked of his advice on how many men should be trained in the use of the bow og'Un remarked, 'One in twenty from each town. Go there, these men will make themselves known."
-Bowman Flavor Text, Myth II
And also, the discription from the manual specifically says that they aren't any good at fighting hand to hand, and you'd think that if they had even some interest in close combat, they'd have picked a thing or two up from the warriors they traveled around with when they were just militiamen.
"...and human militias soon drummed up their own groups of bowmen.
...
If cornered, bowmen can fight with a knife (although this is not their strong suit). To make your bowmen fight hand-to-hand, select the bowman, then double click on a nearby enemy unit."
-Bowman Description, Cast of Characters, Myth II Manual
Obviously, the bowmen preferred using the bow rather than swords, and, since the option was available, would join the army of the Cath Bruig Empire under the Imperial Bowmen rather than as a Heron.