Vest-ectomy

Well now, that depends on a) the level of your sewing skills and b) your threshold for fashion.

These are my thoughts – maybe someone else has better ones.

At the simplest, cutting it off on the sleeve side of the armhole seam, about 1/4 – 1/2 inch away, would be functional, at least for a while until everything unraveled. You could put some sort of sticky or iron-on fabric tape over it to prevent unraveling. But it wouldn't be high fashion.

The next simplest might be doing a zigzag stitch over the cut edges (I'd use 1/8" – 1/4" rather than 1/2"). Again, probably not going to impress anyone but it will be quite functional, and less bulky/sticky than the tape.

Or you could either sew seam binding (folded) over the seam (again, 1/4" or even less), or roll it to the inside (so raw edges are hidden) and topstitch it (for this I'd use 1/2" – 3/4" allowance). Either of these would look pretty nice assuming you can handle a sewing machine, and again, given that assumption neither are terribly complicated.

First question is "what the sizes of the armscyes?" (your first question: what's an armscye? it's the edge of the hole the arm goes through.) If the jacket's sleeves are smaller than the vest, it'll require something to make up the difference. If they're bigger, you have some options.

I think the arm holes are the right size.
I guess I am at that point where there is only one way to find out.
Thanks for the advice DK and David.

From Wikipedia

In sewing, the armscye is the armhole, the fabric edge to which the sleeve is sewn. The length of the armscye is the total length of this edge; the width is the distance across the hole at the widest point.

While the expression "arm's eye" was used in older sewing texts (e.g. Gynametry by M. V. Coleman, published in 1887 by Byrd & Pattillo) it appears that in poor prints the apostrophe and the crossbar of the lower case "e" were indistinct. The neologism "armscye" was created by readers who concatenated the orphaned fragments "arm" and "s" with the corrupt "cye".[citation needed]

Until the beginning of the 20th century writers favoured the original term or at least a more logical variation (e.g. "armeye" in The Perfect Dressmaking System by Ella A. Bennett, published in 1914). However, as self-proclaimed experts copied each other, the term "armscye" eventually became widely enough used by home sewers to gain general acceptance.

Measure before you cut. measure the height, the width, and the circumference of both the sleeve on the jacket, and the scye on the vest. Then, if they're close enough, cut and sew.

(Scye, by the way, is a scotts dialect word, meaning the hole you stick your arm through, with a rather longer history than wikipedia's unsourced claim gives credit for. )

I've done vest-ectomy before – easy, especially if you don't care if it looks a bit ragged.

I think I cut the sleeves off as close to the seam as possible, then there's no fabric unraveling.

Keep the sleeves for booties while sleeping.