Even the AWS D1.5 Bridge Welding Code, with all its concern about fatigue and fracture, doesn't require any optional H or R designation for non-fracture-critical applications, and requires only H16 for fracture-critical applications.
The use of H4 electrodes is NOT standard practice for A 992, A 572 Gr. 50, A 709 Gr. 50 or 50S, etc., or else pretty much all structural welding would be done with H4 electrodes.
Low-hydrogen electrodes, procedures, and practices are recommended, but "low-hydrogen" doesn't mean H4, or even H16. "Low-hydrogen" SMAW electrode classifications are listed in AWS A5.1 and A5.5; the H designations are optional further restrcitions. (For 50-ksi material, the low-hydrogen classifications would be E7015, E7016, and E7018. I'd be stepping outside my comfort zone if I tried to tell you which one of those to use and why, but the bridge welders mostly seem to use E7018.)
AWS D1.1 has lots of info about low-hydrogen practice.
Not that the H4 will hurt, but if the shop has a hermetically sealed canister of regular E7018 on hand, there really shouldn't be any problem with that.
If you want to be as cautious as you reasonably could be, follow the fracture-critical provisions of the AWS D1.5 welding code, though the codewriters' intent is really more for the cyclic loading provisions of AWS D1.1 to be used for your application.
Hg
Eng-Tips policies: faq731-376