Steve it can be flown legally without the spinner. Or a skull cap spinner
Uhhhh, no, not legally, sort of.
According to the Parts Manual, Cessna Part Number 0450516-1, Spinner (a.k.a. Skull Cap) is usable on Cessna 150s from serial number 17001 (the first 150) thru serial number 15072003 (the last "K" model). So the skull cap is not legal on an L or an M.
Can you fly without a spinner? The spinner is listed as "Standard" equipment on the L & M. It came from the factory with a spinner. However, it's not listed as "Required" equipment. The configuration of the cowling on the L & M models is different than the previous models due to the prop extension. So, I guess you can fly without one, but the airflow around that center extension will be all screwed up. No telling what that would do to the cooling air.
I have seen it done with a skull cap, even though the parts manual says you can't.
The 150L in the attached photos was seen at the 2023 Sun n Fun.