It depends on a couple of factors. I assume you plan to play TG and stay TG by your post.
You have already gemmed LFR Shinka Axe with the 500Str gem? I assume that normal mode Axe will not be an option for you? The gem, by my knowledge, can only be received through the quest 1 time, and thereafter it will cost you 10k to buy a new one, should you receive a better version of the Shinka Axe to gem it into.
So assuming that you will not receive any upgrades soon I would suggest the following:
Take Starshatter ilvl 489 in your mainhand and use Shinka ilvl 483 in your off-hand. If there will be no upgrade for you any time soon, use valor points to upgrade your weapons. Upgrade Starshatter (main hand) first as it will have more impact on your dps. The +500 str on Shinka and only 6 ilvl difference to your other Starshatter makes Shinka by far superior to Starshatter in your off-hand.