out of element SSR will never do more damage than on element SR (at least once you get decent elemental weapon grid going), so the only reason to bring an out element SSR is if she has other ways to contribute to the team (like Sol's healing and unique C-frame atk debuf) As for your situation, Shiva's atk buff is exact copy of Arthur's atk buff, so once you can get that as an EX skill on your soul, then get rid of Shiva on your light team. Tyr has def debuf, but its only 10% A-frame (Gawain EX skill is 20% A-frame, but then you cant get Arthur's atk up, so its up to you what to get) However Tyr will still hurt quite a lot, if you burst her while enemy is stunned.
Considering all that, and since debuffs>buffs, i, personally would go Sol+Joan (-40% atk debuff, and if we add to that Jorm's summon effect, we get to atk debuff cap of -50%) with Gawain's def debuff, Belobog (def buff) Shiva (atk buff) and Artemis if you have multiple "Shining assault" skills, or going against wind enemies, otherwise Tyr.