How? You might ask.
The answer is by using the test server Tribble, the only downside is you need at least one key and one lockbox (Infinity is best) to copy over (I would suggest a minimum of 50).
As described in the link above, you download the server from the client launcher and you go onto the arc transfer page, which will allow you to copy a character onto Tribble. Make sure that character has Lockboxes and Keys! You can copy the same Character multiple times, which is what I have done. I would suggest copying enough so that you end up with 250 keys on Tribble.... and no sadly you can not copy them all back! This will not affect the live server at all and the Devs can wipe the test server at any point they choose.
You will need a lot of keys and lockboxes on Tribble if you want to try multiple ships - it also gives you an idea of the type of ratio you might expect for a T6 Ship drop rate.
If you have an infinity promotion box you can try the same tactic by copying your character then trying the different ships. You can not try C-store ships - in fact the C-store is not available on Tribble.