Hallo Abhishek,

ok, I understood. You don't need long term stability. And you would not need exactly 1.25V. 1.25V + 25mV would also be ok, but it should be constant during the measurement session, right?

Well, in the case of using a relay keep an eye on contact material. Don't use cheap contacts. There are some very good relais available, which are well suited for dry switching. They have a massive gold surface and are put in some inert gas. They guarantee best performance, even after many switchings.
Don't use silver contacts. They are well suited for high current switching, but need a minimum load for making sure contact. And if contacts are not put in inert gas, but normal air, contacts are oxidized (silveroxid) or sulfidized (silversulfid) after some months. Especially when running in your 'tropical' environment in India.

May be that the use of a FET with very low drain source on-resistance results in superior performance. But also the use of BC317 would be appropriate, I think.

Good luck,
Kai