Registering Marriage in Germany or Singapore?

Religious marriage certificates are not recognised in Germany.
Therefore I would really recommend you use the normal Singapore ROM.
(That's where we married, too, and we never had any problems with formalities or recognition.)

All marriages in Germany must be performed at the Standesamt (family registry) by a government official. Where you have a party or optional ceremony afterwards is up to you. Many rent a location like restaurant, hotel, church, temple, etc. for it. No idea if mosques are available, too. We had Turkish weddings in the neighbourhood, which were huge affairs with many guests and loud music - so some do it at home as well.

One needs to have a state sanctioned marriage for it to be recognized. In some countries a religious held wedding will fulfill the State requirements and also be seen as valid. In most countries one gets legally married in a civil ceremony and the religious wedding is a ceremonial thing that is independent of civil legal significance. Singapore has people of many religions but is not a primarily Islamic country yet appears to now recognize such Islamic ceremonies but there are rules and restrictions. 

I am posting a link to a Wikipedia article about the marriage laws in Singapore.
https://en.wikipedia.org/wiki/Matrimoni … _Singapore

Singapore seems to recognize Islamic weddings but only if both partners are Muslim. A Muslim and a non-Muslim can marry in Singapore but only through a civil ceremony. And even if your German fiancé is Muslim, as a foreigner, permission must be given from something called the Ministry of Manpower. From what I’ve read, they only want foreigners marrying in Singapore if they are, or formerly were, living there with a work visa. Non-Singapore residents can also marry there but at least one of the partners has to spend at least 15 days there prior to the wedding. It sounds like the rules are to keep people illegally working in Singapore from getting married to legalize their situation. 

Germany will accept what the civil authorities of Singapore require within its domain. Thus if you get properly marreid in Singapore it will be recognized in Germany. If you get married in Germany you have to do it at the Standesamt. Any Muslim ceremony you wish to have in addition is your choice; just ask at a mosque. There are over 2 million Muslims in Germany, mostly of Turkish decent, so this is not a uncommon situation.

The expat.com expert for Gremany Beppi is married to a woman from Singapore and has lived there, so maybe he can give you more detailed information or insider tips.