bro when i was in goa, i had only jio 4g access and it had nat 3 type. i did gaming for 5 days of fifa 17 (this game requires a serious level latency) and it worked very smoothly. as far as i have seen, nat type doesn't make that much diff as much as stability of your connection does.
your connection has to be very stable for ps4 gaming or you are in a serious pain.
right now i am in jammu and bsnl connection is rock solid for ps4 gaming, jio is heck not. and airtel 4g is hit and miss. phone hotspot with airtel 4g doesn't work however if i use the same sim on airtel hotspot device gaming is much stable compared to bsnl broadband..
even if u do get public ip (as i guess your wired connection has put u under server which gives u netted IP) , public ip won't help in my experience. it's your connection that has to be stable. and btw railwaire if i remmeber correctly has their 90% of IP's banned/terminated on PSN network lol. you can search abt it.