Where I draw the line, having got this wrong once: anything with interfacing, padding or a lining goes to the cleaner.
The reason is that you cannot see what you are risking. Interfacing is glued or stitched inside the collar, lapels and front edges, and when it gets wet the adhesive can let go in patches. What you get back is not a shrunken garment, it is a lapel with a bubbled, rippled surface that cannot be pressed out. It does not fail while it is wet, it fails as it dries, and by then there is nothing to do.
That is your blazer and quite possibly your coat.
Two other things worth knowing:
"Dry clean" and "dry clean only" are different labels. The first is a recommendation, the second is the manufacturer saying they tested it and it failed. Not a guarantee, but the distinction is real and it is worth looking at which one your items actually say.
Ask the cleaner rather than assuming. They will tell you honestly if something does not need doing, and many will do a press-only for much less than a full clean: which for a coat that has lost its crispness rather than got dirty is very often the actual fix, and it is a fraction of the price you have been postponing.