Also not a lawyer, but in my understanding...
Your band doesn't need Skynyrd's permission to play "Sweet Home Alabama" so why would you need your ex-guitarist's permission to cover his songs? Assuming that he's registered the songs with BMI or ASCAP, then he gets a royalty (paid by the venue, not the band) every time you cover his song. It's a win-win for both parties. Your covering these songs, puts money in his pocket.
(disclaimer: not a lawyer)
Legally, SOMEONE needs to get Skynyrd's permission to play the song, and pay royalties. In the case of virtually all known artists like Skynyrd, that's handled by a blanket license purchased through BMI or ASCAP, and customarily the venue does it, but only because bands are ephemeral entities and rarely have any money anyway.
Technically, if the OP's former bandmate were the sole owner of the songs in question, they would indeed need his permission to play them, and if he hadn't registered them through an agency like ASCAP, anyone wanting to play them would need to get his permission directly. But see below...
Unless he registered all of the songs he co-wrote at copyright.org, or the publishing rights with one of the organizations
@Staredge mentioned, he doesn't have a leg to stand on, legally speaking.
That's not the case. Any creator of a work has copyright in that work regardless of whether they register that copyright or not. The purpose of registration is to DOCUMENT a copyright claim, which makes it easier to prove if there's a legal dispute. But the rights exist regardless, by the bare fact of having created the work. ASCAP and BMI, mentioned by
@Staredge, have nothing to do with legal copyright claims; they are agencies to sell blanket licenses to perform songs and collect royalties.
I'm not a lawyer, but I did some homework on the topic, and here's how I understood the part about control over own work.
If said guitar player was the only songwriter, then the songs are their sole property, and can do anything they want with their work, including sue any musicians who play their song if they so decided.
If a song has multiple songwriters, then it is owned by every contributing party, BUT the control over it works as if every one is the sole owner. What it means in practice is that if 5 people write the song, 4 of them who claim 99% ownership say they don't want it to hear ever again performed, but the 5th with their last percent says go ahead, then that one writer's approval basically overrides the others' decision.
It's a clever mechanism; imagine how many songs would have disappeared over a quarrel if not for this.
If your ex guitar player wants you to stop playing songs you wrote together, first they'd have to claim sole songwriting credit, and if all of you wrote a part and have it documented somewhere as such, then forget about the threat.
The only instance I know of where one songwriter blocked the others, is Josh Homme claiming sole ownership of Kyuss, and the remaining two, John Garcia and Brant Bjork, simply don't have the cash for lawyers to fight back. He didn't win, he just locked the others by having more cash to keep disputing. This happened when John and Brant decided to reunite Kyuss ca. 10 years ago, and began performing with a different guitar player when Josh declined.
This is correct. Performance or recording of a song requires the consent of the owner of the song, normally its original creator unless there's a contract indicating otherwise. If the OP's ex-bandmate had solely written the songs, then he does indeed have the legal right to deny the others permission to play them.
"Song" is normally not defined as all the constituent parts of a recording or version of it, but usually the lyrics and melody (think how many versions of "Minnie the Moocher" Cab Calloway performed over the decades, in a gazillion different genres. Even if it was in a reggae or country or calypso style, it was still "Minnie the Moocher" and the same people held its copyright).
If a song was created jointly by several people, they are all joint copyright owners of it. In that situation, EACH copyright holder has the authority to permit a recording or performance of it without the agreement of the others. However, ALL are owed royalties on such performances. Parts of an arrangement of a song (e.g. a bass line, drum beat or rhythm guitar part) do NOT carry separable copyright - you can't deny a copyright holder in the song permission to use the part that you came up with for it when they exercise their right to perform the song.
The OP said each of the band members wrote their own parts. If this were to go to court, it might well be the singer (if this isn't instrumental music) might be decided to be the sole owner of the song if they were the only one to write lyrics and a melody.
This is all on the assumption that we're talking about American law here. Overseas there are some differences. It's also assuming that there are no written agreements in which people agree to forego their rights (e.g. a studio musician would often sign a contract accepting that, whatever contribution they make, they claim no copyright in the work, in exchange for the fee they're paid for their work).
Also, as several people have said, this is all technicalities. Royalties are pennies per performance. Unless the OP's band is putting out mega hits (in which case they probably wouldn't be coming to TB with questions, they'd be asking their record label's legal department), there's nothing at stake and threats to sue, etc., are just blowing hot air. These kinds of threads come up on TB pretty regularly when some drama queen storms out of band practice yelling their head off.