I just found this thread regarding GW downgrade (NOT the 2.1 Downgrader which is just crap)
https://gbatemp.net/threads/gateway-downgrading.378195/
It seems you cant downgrade a 2ds to 4.5.
However why dont you upgrade to 9.0/9.2 and install MenuHax to get rid of using the Browser everytime?
(sorry I have actually no idea if this will work since it has been ages since I installed GW on my o3ds and n3ds. I also dont now if sth could happen to your Savegames)
P.S.: @ Gateway haters: I'll just copy this from the link above (about GW downgrading from 9.0 to 4.5): "Report based on thread up to Page43:
100+ successfully downgraded consoles and 0 Bricked console, 1 unconfirmed brick(page 18)so far."