one outopilot on MEL-one more reason to check very carefull the weather -metars,tafs,metars history.I would'nt dispatch with one a/p u/s if any chance for a cat 2-3 app.And we are talking about the 737,not 777,so a shor-medium flight .You should be able to predict the weather with a high degree of accuracy for sucha short period.If in a situation like you said-cat 2 ,I'll go for manual land,instead of sch autoland..Keep in mind that in case of fire many of the systems or instruments are prone to fail ...
If cat3 in force...I'll try it also manually....yrs ago we did a lot of blind landings (curtain on the PF side) with alt calls from PM-in can be done right to touchdown,no problem.
We can imagine a lot more scenarios,but you have to avoid getting yourself in the corner by any means..
brgds