If the picture shows complete L2 topo, then RTG on switch4 for green links should work fine.
Switch4 will break the loop by using only one interface from RTG at a time (packets, BPDUs on backup interface will be discarded).
You don't have to disable STP on links between switch1-2 and 1-3. Only requirement here is to disable STP on switch4 for links participating in RTG.