Can Major Rhymer's ability be used on bombs/mines/charges or are they not considered secondary weapons? Thanks.

Can Major Rhymer's ability be used on bombs/mines/charges

No, as you point out they aren't considered to be Attacks. Also they don't have a listed range so there's nothing for him to change.

Secondary Weapons are cards that have the "Attack:" header. Bombs and the like don't have that, so aren't secondary weapons, so Rhymer does nothing for them.

Worth noting that the same goes for Krassis Trelix (when attacking with a secondary weapon you may re-roll 1 attack die) & Captain Jonus (when another friendly ship at range 1 attacks with a secondary weapon, it may re-roll up to 2 attack dice). Doesn't work for bombs.

Sidebar; I'm thinking those two will make a killer combo...

Worth noting that the same goes for Krassis Trelix (when attacking with a secondary weapon you may re-roll 1 attack die) & Captain Jonus (when another friendly ship at range 1 attacks with a secondary weapon, it may re-roll up to 2 attack dice). Doesn't work for bombs.

Sidebar; I'm thinking those two will make a killer combo...

You've got terrible luck indeed where 3 re-rolls will be needed on a consistent basis. I'd rather go with a Bounty Hunter when flying next to Jonus, and use the 3 points for a crewman (Recon Specialist or Rebel Captive)

I figure it's like a gun, better to have it and not need it than to need it and not have it.

I was thinking HLC & maybe Merc Copilot for Trelix, 4 attacks at any range w/ rerolls at 2&3, Jonus to buff & use missiles or topedos of some sort & maybe a couple academy TIEs to run interference & keep the enemy @ range. Haven't had a chance to try in-game yet so it's all speculation.

Just realized I've taken this way off topic, sorry OP