Ceremony only church-like venue Glasgow

You won't get a non-religious ceremony in a church - that's sort of the point of churches!

Civil ceremonies do largely tend to take place all in one venue or be a registry office followed by reception in a different venue. The money in weddings is all in the reception (food, venue hire, bar takings etc), so very few places are geared up just for the ceremony. Some historical buildings just do the ceremony. I think some theatres might just do the ceremony as well, if you have anywhere like that nearby?

I agree I don't think you will find any church that will allow you to have a non religious ceremony! If you don't want a registry office you could try hotels, museums, aquariums, maybe approach the national trust who may have buildings, outdoor spaces or ruins. Is there no chance you can hold your wedding at your reception venue? In some instances you could need to go to the registry office with or without guests to make your marriage legal but you can also do this without your guests and have your non legal wedding as your ceremony.

Is there a reason the reception venue doesn't work for the day? I can't think of anywhere - in Glasgow - that would do reception only.

If you want to move city the Botanic Gardens in Edinburgh might do ceremony only?

Oh wait - what about the science centre? They do corporate events so they might let you come in with a celebrant depening on the day.