The availability of options is limited by the rimfire action you have and your ability to google. The Savage will be more limited than a Ruger, but options exist. You will most likely pay more to upgrade the Savage than repacking it.
If you want the benefit of the chassis system you need to go aluminum. Polymer can be lighter, but the lighter options would be more likely to have flexing issues which defeats the purpose of the chassis. I didn’t find any true chassis options that were polymer. You could probably find a stock that looks like a chassis that is polymer which may be a better fit for it sound like you are asking for.
Chassis systems that can be set up for the Savage MkII action.
https://mdttac.com/us_en/lss-rimfire...is-system.html
https://www.rigidalloy.com/srf_chassis.aspx
http://www.accurateriflesystems.com/...-tactical-prs/
PDC Custom is supposed to have one in the works as well.