According to page 175, non-Legion weapons must be modified to be used with Legion Power Armour. Does this apply to heavy weapons commonly used by CSMs, like the Autocannon, Lascannon, or Missile Launcher? What about a Force Sword (there's no Legion version)? Do these modifications have any Availability or other restrictions, or is it just a simple matter for someone with Trade (Armourer) and a few basic tools?

For large things its probably no issue that even needs the armourer. The Autocannons are probably manufactured with bigass hands, power-armor or recoil gloves in mind to begin with.

Something human-sized but expected to be wielded with such upgrades, like those arbites 1d10+9 shotguns, are probably "just tear off the trigger guard so your finger can fit there" levels of minimal work.

If we're talking a human version of a legion weapon, that definitely needs some work done; they've been split into two scales specifically after all.

Where I'd draw the line is tiny stuff. A compact laspistol [why would you even?] is going to need some serious fixing up, given its probably the size of that marine's finger.