Are they the buttons with holes in them? If so, maybe get a curved needle (like for upholstery) and you could probably use that to hand stitch it on. Think that would be easier than taking apart.

Do the buttons actually work, ie, does the sleeve unbutton? If it doesn’t I’ve seen even good suits with the buttons sewn through the lining. If you still don’t want to sew through the lining, turn the jacket inside out and look at the sleeve lining seam itself. Usually on the left sleeve there is a hand sewn part of the seam which can be opened, stick your hand down to the sleeve that the buttons are in then sew your button with one hand inside the jacket, one out, then resew lining.

You should be able to unpick the seam in the sleeve lining, sew on the buttons and then slipstitch the seam closed.

Stitching through the lining is acceptable. You would probably be able to stitch through the sleeve layers and leave the lining free if you're careful. Before you pull the needle all the way through, check to see if you've picked up any of the lining. If you have, very carefully pull the needle back slowly, and pull the lining free.