I think lines sleeves are actually pretty simple to shorten, as long as you take your time I don't think you could ruin your coat. I'll try and describe the process so you'll have a better idea if it's something you feel capable of!
I'm assuming it's a plain sleeve, no vents or belts or buttons or anything:-
1. mark the point where you want the sleeve to end using tailor's chalk, and make a note of (a) how many inches the sleeves need to be shortened by and (b) how much the outer fabric is folded into the inside of the sleeve (usually 1"-2").
2. you need to get in between the lining and outer fabrics - on some coats the lining is not sewn to into the main body hem, so you can get in that way, otherwise carefully unpick a few inches of the seam of the sleeve lining, sort of from the elbow down (you'll top stitch this later -- check to see if there isn't already some top stitching on the seam that you can undo).
3. Turn the sleeve out through the opening you just made, make a note of (c) the seam allowances, and unpick the lining from the outer fabric at the end of the sleeve.
4. Mark on the outer fabric, from the end of the unpicked sleeve: (a) the number of inches to be shortened, then another mark (c) your seam allowance (you'll sew along this line), then mark (b) to allow for your turn-under. CHECK that this mark matches the position of the one you made at the very beginning! Mark these at a few points around the circumference of the sleeve. (ALTERNATIVELY, when you make that very first mark on the outside, stick a pin in it. Then when you're marking the inside, you mark towards the raw edge first your turn-under, then your seam allowance).
5. Mark the lining fabric the number of inches to be shortened, and mark seam allowance.
6. Cut the outer & lining along the marks you made closest to the raw edge.
7. This is probably the trickiest bit: Align the seams of the lining and outer fabrics (it sometimes helps to turn the sleeve right side out, add a pin, then turn it inside out again), align the raw edges right sides together and sew along your marked line.
8. Turn the sleeve right side out and press so that you have the correct turn-under (I usually re-measure it and add a pin). Turn it inside out so that you are on the right
side of the lining. Pin the hole you made closed, then top-stitch it closed by sewing as close to the edge as you can possibly manage.
9. Now repeat for the other sleeve!
That's how I do it anyway. I hope that makes some kind of sense! If you look at that and it makes you want to run for the hills, then I'd recommend getting it done professionally
The key really is to measure carefully, so you can be confident you'll have the right hem and turn-under. If you aren't taking much off the length, you could even get away without cutting anything, so if you do mess up, you only have to unpick and re-sew!
Anyway. Whatever you decide, I hope that helped & good luck!