Definitely get out onto to some fleets. That alone will help you, and you get that sense of being in a combat unit (for those with military combat arms experience, you know what I'm talking about).
One thing I can suggest is put yourself in a
Kobayashi Maru scenario (the unwinnable scenario, or at least the unsurvivable). As a Uni member you'll need to do this on an alt. Basically go out and attack someone in highsec who isn't a legitimate target (they are not flashy to you). Do this in a cheap ship with a cheap fit and not much ammo. This is known as suicide ganking. Attacking unprovoked, with the 100% guarantee that you'll lose your ship. You may even kill your target, depending on what you attack. This will help you get over your risk aversion. And it may even give you that taste of blood and the swagger of a dirty pirate
.
Your ship is ammo. You expend it.
You can also fit out a decent, but inexpensive combat frigate and head off to a lowsec region which has Factional Warfare on the go. There are plenty of systems near the Uni HSC and HQ that qualify. Jump into a system, check local, set up some safes, and once you have a few, start to d-scan the FW sites. Concentrate on the Novice and Smalls mainly. Novice sites are limited to T1 and Faction frigates, Smalls are limited to destroyers and frigates. What you're looking for are solo pilots in those sites. If you spot one you can warp into the site (at 10K, so you don't tangle on the Accel Gate), and then slide in via the Accel Gate. You'll land right near the FW beacon. You may get lucky and catch your prey right there, or at least in the site. You may find they are waiting there deliberately so as to get some fights.
Do worry about winning. You're more than likely going to lose. And there's nothing wrong with that. The most successful people in life are the ones that have gone out and failed time and again, but they simply got back up and kept pushing forward. The same can be true of PvP in EVE.
Another great place for you to learn is on Sisi (Singularity), test server. Stations there are seeded with most modules, charges, rigs, etc., with the exception of deadspace, faction (I think) and officer mods. And everything, including ships costs 100 ISK per unit. You'll want to get a handful of friends on with you. And just get in a do it. You'll blow up lots, and it won't matter. You'll learn lots and have fun, which does matter
.
And again, get on to some Uni PvP fleets. You'll learn a lot and you'll have fun.