Easiest way is to join a faction and ask the leader to organize a Testing with a Force-Sensitive organisation - Jedi Academy usually. It'll depend on how many members want it done and if it's been done recently, but if you're lucky you might get tested within the next couple of months. Of course, it could also take up to a year, or even more, so it's better if you take it without much of a hurry. It's good that you already face the fact that it's most unlikely.
no not really there are other things that use non projectile weapons. Force Pikes, Vibroblades, and Whips to name a few. Besides I am pretty sure when you become a jedi you get some sort of lightsaber combat skill.