You only have to deal with the weeds in block paving...the root system for moss is nowhere near as deep.
Glyphosate (the active ingredient in many weedkillers including Roundup) needs 24 hr to take effect although signs in the plant itself (initial reddening of he leaf) can take weeks. Spray one day ..wash the next.
Glyphosate works by preventing the plant producing amino acids...so the plant "starves" itself to death.
Because of the way it works it is generally considered to be "safe"
Add fairy liquid to your weed killer mix...you will then use less as it "sticks" to the leaf of the weed.
Flazasulfuron could (if you wish to break the law) be added to your mix, this is a post-emergent residual herbicide ,it works by prevent seeds germinating ...keeping your block paving "weed free" longer.