I don't have any personal experience with putting standard OEM wheels onto a Z4M, however I have put larger brakes on my Z4 (325x28mm with brembo calipers) and my MV2 style 135 wheels required spacers to clear the calipers. The stock Z4M brakes are 345x28mm, so you would likely run into fitment issues against the front brake caliper when using a style 108 wheel.
In terms of the rear, the brakes are much smaller so likely no issue there. The issue at the rear will be the massive offset difference. OEM Z4M wheels (style 224) have a rear width and offset of 9J ET30. OEM Z4 wheels (style 108) have a rear width and offset of 8.5J ET50. This means the inboard rim will sit 14mm closer to the damper strut and the outboard rim will sit 26mm further inboard than stock Z4M wheels.
I am not sure you will find many people who have actually put standard Z4 wheels on a Z4M, usually it's the other way around. Personally I wouldn't do this as you would need some massive spacers on the rear to get the wheels to look normal (flush) again, but remember that's only my opinion.