There are some models to compute single arm meta-analyses. I would suggest the arcsine transformation, but it depends on the specific topic and studies.
To chose appropriate selection criteria is particularly important to minimise the risk for publication bias.
Your ability to answer questions will be restricted due to the underlying data but provided you can combine "like with like" you should be able to do a useful analysis, especially if you can obtain individual participant data. Without individual data however, the value of any analysis you could do would be limited.
I am facing a paper with a single arm study meta-analysis. I understand that you can perform a meta-analysis to compare single arm studies about different treatments for the same condition. I also assume that you can also do it to compare treatment Vs. no treatment. Here, we have a study involving 5 case series of patients treated with one particular type of surgical anastomosis with no comparison. Do you think it makes any sense?