Weed membrane (say Mypex) excludes around 95% of light and that is enough to kill most weeds, especially when allied to compost mulches. So you could use it, however cutting such membrane results in many horrible strands of polypropylene.
I do not recommend this approach because, the way you describe it, you have membrane under all the path mulch of slabs and chippings. Some time in the future, this will be a problem for someone who is gardening differently – its extremely difficult to extricate membrane once it is half buried in soil.
I would simply roll up the whole sheet, for reuse elsewhere.
