As you have already found, records at this period can be difficult to access. You would probably have to wait 75 years for the coroner’s report to be released.
By far the best way to go will be the newspapers. The inquest is bound to have been reported, probably in the Yorkshire Post, and/or a more local paper. Relatively few newspapers from this period are online.
As you will know the area and the exact inquest date (from the death certificate), it shouldn’t be too hard to search the newspapers manually, either at the British Library in London or at Boston Spa. If you can’t get there, you may need to engage a researcher to help you.