It's the same with RDM. We have no native staff skill, yet we're are able to equip a number of different staves. Any skill we have will come from our support job (which means we'll be unable to skill-up on our main, and like everything else from our sub, it will be gimped to half our main's level). BLM/RDM is probably the easiest way to get sword skill, but it's not really worth it.

If your job has no skill in the weapon, it's not worth using for melee purposes by any means. Without a native skill level, it means you're only going to get something like 8 natural attack in the weapon. All other bonuses to accuracy and attack will come exclusively from DEX and STR modifiers and whatever you can get in gear and food. This means you'll be horribly inaccurate with the weapon, and even when the blow does connect, it's not going to be worth much.

BLM gets some skill with a scythe, I believe, so that's worth pursuing if you really desire to melee at all on your BLM. More often than not, though, BLM is just too damn squishy and lacks any significant native defensive spells to be an effective melee job even solo. BLM can solo a lot, but it's usually by making things go boom.