Many claims are so that among the army skulls were adopted first or most common along the men of Kev. Os 4. I have been researching the matter and it seems the case. I took some more look on the matter and I found out that other units using the skull emblem had officers from the Winter War era Kev.Os. 4.
Central person here is ratsumestari (later Majuri and Everstiluutnantti) Alfons Sundblad, commander of the I/JR 46. An old cavalry officer with years of experience from URR and he had led KevOs 4. He was very flashy officer wearing cavalry insignia, cavalry trousers, skull helmet and commonly held a baton.
Juha E. Tetri's book about the Finnish army unofficial insignias lists that the I/JR 46 used black skull hat badge and that the JR 46 as whole regiment wore an yellow-white-black twill insignia on their left shoulderboard. Their unofficial "rähinäremmimerkki", belt badge was an swastika with similiar color combination on the middle.
Some sources claim the I/JR 46's unofficial nickname was "Pääkallopataljoona", skull battalion.
Then we start to approach the most known skull painting related picture from the Continuation War (Signal cover). It is usually attributed to the 3. Prikaati, people including myself saw it because of the twill on the shoulders.

Though from what I've seen the original picture seems to be black and white and the colored version appears to be colorized later (correct me if I'm wrong). JR 46 indeed had similar twill insignia, however it was colored yellow-black-white instead of the blue-white of the 3rd Brigade.
JR 46 unit diary lists that they were having combat exercises during the time the picture was taken (1st June, 1942)
19th April, 1942 the JR 46 had an oath ceremony held at Valkeasaari which I/JR 46 attended. Skull helmets are to be seen in pictures and while zooming in you can see the typical twill insignia on picture 84421.
Details of the 84421:

Sundblad himself appears in pictures 84417, 84418 and 84423 while wearing Kev.Os.4 styled skull helmet. You can also see other skull helmets on the background in 84417 and 84421.
Attention now shifts to the 4th June, 1942. Parades were held for Mannerheim's birthday and I/JR 46 attended the parade which their unit diary lists. So any mention of Pajari's troops wearing Skull helmets could be attributed to the 1st Battalion of Infantry Regiment 46. (as HerrHetzer noted in the another topic)
Diary entry telling of their attendance in the parade:

Interestingly enough SA-kuva ID 91739 has an officer whom appears to wear the insignia of JR 46 and his "rähinäremmimerkki" appears to be the Swastika of the JR 46. I have not, however identified his helmet marking.
Details of the ID 91739:

As mentioned in the other topic by others, pictures 91741, 91742 and 173233 contain Skull helmets and picture ID 173235 has similar marking to the 91739.
Sundblad as Lieutenant Colonel again appears in picture 156132 at Vuosalmi, picture taken 20th July, 1944.
Detailed look on that:

What is of interest is that everyone again excluding the Jaeger brigade officer wears the same twill insignia. What is though of oddity is that the Jaeger Brigade captain has the belt badge of the JR 46 which is a swastika. Sundblad also wears the hat badge of the I/JR 46. You can also see an skull related badge on the lieutenant on the right on his trousers.