Its even possible to get MkIV on Earth's Spacedock. All you need are the Badges of Exploration you get for the Cluster Exploration missions.
When you have some (MkIV weapons are for 77 badges) you go to ship requisition and talk to the vendors there. They have MkII to MkX and you need badges 1st to 5th grade to purchase the items.
The Tier II ships do come with Mk II items. The easiest place to upgrade is up the ramp in the shipyard on Earth Spacedock. There are vendors here that have items of all levels. They do require the exploration tokens from Delta Volanis for the first upgrades. Hope this helps.