Hello HWBY,
The records I have only go up to about 1917, so I can't help with the 1941 request, sorry.
Here is a list of those people interred in plot E1676 of Cambusnethan cemetery, you will find your William among those present!
MARY WEIR, housewife, Wishaw, aged 69 years, married.
Parents - John McCulloch & Sarah Robertson.
Interred 1st October 1907.
Plot owned by William Weir, engine keeper, 51 Berryhill Rows, Wishaw.
ALEXANDER WEIR, waggon worker, Wishaw, aged 42 years, unmarried.
Parents - William Weir & Mary McCulloch.
Interred 1st August 1908.
JEANIE D. WEIR, Wishaw, aged 7 weeks.
Parents - William Weir & Helen Winters.
Interred 26th May 1913.
WILLIAM WEIR, pitheadman, Wishaw, aged 75 years, widower.
Parents - James Weir & Mary Hamilton.
Interred 1st August 1914.
I may be able to find the later interments for you but it could take a couple of weeks. Could you contact me again as I will probably forget!