I don't have a HWK, for instance. Can I replace it with like a Y-Wing, or do I have to have one?

And is there an Imperial format? I'm looking through it and I don't have three-quarters of the Rebel ships I need.

Realistically you can get away with just the base. Or stick any ship on the peg. The stats are easy enough to look up.

usually between all players our group has everything though we short a Decimator for a while.

Many TIEs are recommended!

Just companion ship

Need? No.

Is it more flavorful to have all the ships they prescribe? Yes.

To participate in a HotAC compaign, all you need is the ship you plan on flying. If you are running the campaign, or sharing the load with the group, you will need much more. Especially Ties, their numbers scale up depending on how many pilots are on mission.

29 minutes ago, Rinzler in a Tie said:

Just companion ship

That would be this little guppy, am I right?

1 hour ago, Celestial Lizards said:

And is there an Imperial format?

Why yes, yes there is.

We started our group recently with 6-10 Ties, an Interceptor, 2 X Wings and 2 Y Wings. With 4 players for most missions.
Its really fun!

The only ting that's awkward to proxy is the rebel transport due to the base size and movement template if you do not own another epic ship. Otherwise as said above; you can use and ship and tile so long as it has firing arcs and just pretend it's a HWK/TIE fighter etc.