First time driving for 4 months on Wednesday and I scuffed the end of the driver's side mirror casing getting it out of storage.... the scratches aren't deep but they are through the black paint and show. Any ideas if they can be polished out with some sort of black polish?

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I think the general rule of thumb is if you can feel the scratch with your finger nail it isn't going to polish out - otherwise a good cutting polish will certainly reduce the appearance of the scratch, if not the scratch altogether. FF 4.4 V8 Soooo looking forward to this bad boy
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Looks like the scratches have just gone through the clear coat. If that's the case, use a smidgeon of something like Farecla G3 scratch remover , available from Halfords, or cheaper online, followed by a polish and wax.
I'm not an expert but this worked for me on some bramble rash . Scratch remover reduces the clear coat so use it minimally on the damaged area.

You're not removing the scratch !

Just remember that 'polishing out' a scratch means rubbing down the surrounding area to the same level as the scratch bottom. You'll be left with very little surface lacquer (if any) after that depth of scratch is made invisible

the cover is easily removed. It won't be very much to get it painted correctly.

Take the mirror cover off & have it painted.G3 scratch remover will not remove that.

Andy. Andy.
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looks too bad for a polish out,

there is polishes that disguise scratches, by filling them with black residue, but will come out and not leave a invisible finish, you'll be better off, popping it off and a respray

There is methods also were you fill the scratches with a fine 'model' brush and slowly build up layer after layer to blend it into the surrounding paint, then sand back and machine polish to a smooth finish

Popping it off is the best option, for time and finish

Tim in Scotland wrote:

First time driving for 4 months on Wednesday and I scuffed the end of the driver's side mirror casing getting it out of storage....

is this the reason why they uses a harbour "Pilot" to park your ship Saves them buffing a few scratches out each time