1.4003 was a DIN designation. DIN designations have been replaced by ISO, in this case 3Cr12. It seems to me that 3Cr12, which as you said is a ferritic stainless, is equivalent to AISI 410, also a ferritic stainless with 11 - 13% chrome.

If this is the case, GTAW is far better that SMAW, that uses covered electrodes, also called stick eletrodes. Stick electrodes were used to weld stainless when GTAW (TIG) welding wasn't fully developed yet. Nowadays there's no reason for not using it.

Back in my days of erector engineer we had to weld the AISI 410 inside lining of a crude oil vacuum tower, and we did it with E 308-16 stick electrodes. In those days, very few welders were skilled in TIG welding. We had a hell of a time (if you allow me to use rude words) in doing it, and I can explain the reasons in another posting.

Neither preheat nor postheat are required when welding stainless steels.
Warning! For welded constructions, it's better to use 304L rather than plain 304. 304 is prone to sensitization.

Giovanni S. Crisi
Sao Paulo - Brazil