The registers for St Mary's Newark are conspicuous by their abscence.
As you say, many of the usual sites have transcriptions - I think many of these are from a Phillimores printed book. But nobody has the actual register.
It may well be still held at the church - a few still are, or at Nottingham Record Office, although I had a search on their catalogue and didn't find any mention of it.
However, familysearch DO have a film of the Bishop's Transcripts, which is locked, so only viewable at an LDS library or affiliate library.
Luckily my local library is an affiliate library, so I had at a look at it today.
Here is the part with their marriage listed.
Although it seems to give no further information, it is interesting to note it seems not to have been by licence. Several others on other pages say 'lic' next to them. This means it was probably by banns.
Quite often, widowers obtained a licence to marry a subsequent wife. I can't say this was a hard and fast rule though, so I wouldn't take it as a solid piece of evidence he wasn't a widower.
Perhaps an email to Nottingham Record Office, and St Mary's church themselves might be the next step to see if they can shed any light on where the registers are.
Added:
So for some reason the attachment button is not working - perhaps it's because this post is on a Lookups board. I don't know.
If you'd like to send me a PM with your email address, I can send it to you.
You are not allowed to post personal email addresses on these posts.