Croeso i’r fforwm, Sara! 
I am also a relative newbie to learning Welsh and have yet to speak any Welsh in the wild. However, I do have experience of having a ‘speaking fear’ in other languages – German (which I am now fairly comfortable with) and Spanish (in which I am a walking, talking disaster…) so hopefully I can help you out a bit!
If I may add another analogy into the mix – think of speaking like skydiving: Before you jump is the most absolutely terrifying part. You don’t want to do it; it would be easier just to stay in the plane. There are only two ways of then ‘persuading’ yourself to jump out the door – do it before you think too much about it, or get someone to push you!*
Once you jump, you’re on your way and maybe you’ll realise it’s actually quite fun, and not so scary at all. (My analogy falls apart when it comes to the deployment of the parachute / reaching the ground, so I’ll just leave that bit out) 
There is no way to prepare for actually doing a skydive (other than learning the safety procedures – which, in this now very tenuous analogy, can be stock phrases like ‘I don’t understand’ or ‘Can you repeat that please?’ etc.) – you’ve just got to take the plunge and do it. It is impossible to gain speaking confidence before you start launching yourself into real-life speaking situations – so all you can do is dive in at the deep end (oh dear, I’m mixing up metaphors awfully now!).
But the main thing is: yes, it’s scary and yes, it’s difficult – but that’s what makes it worthwhile. Yes, you will come away from some situations feeling like an idiot (I’ve been there many times…) but other times you’ll come away completely elated! And those moments will propel you forward and give you more confidence. Better to have some cringe-worthy memories of trying to speak Welsh than to never have tried at all.
*If you find that you do want to be ‘pushed’ into speaking in the wild, you could use this forum to help – e.g. post a mini report every week of where you have spoken Welsh, so that you start to push yourself to do so instead of falling back into the English ‘safety net’.
Some suggestions for putting speaking into practice:
– Build Welsh-speaking habits into your lifestyle: if your local shopkeeper speaks Welsh, for example, build up the habit of talking to them in Welsh. The first time will be totally nerve-wracking, but it will get better after that, and after a while it will become the norm for you to speak Welsh whenever you’re in that shop – your brain will build up the association so that eventually, speaking English in the shop would just seem strange.
– Join a club or a fitness class or something else that is run in Welsh. Very scary to begin with, but hugely rewarding! Again, your brain will build up these associations so that speaking Welsh truly becomes a routine. (Plus you’ll learn impressive specialist vocabulary!)
– Being upfront about the fact that you’re a learner can help, because as soon as you make that clear, you’re taking the pressure off yourself to say everything perfectly. To use my Spanish as an example: even though it was completely obvious to everyone by my accent and my general stumbling awkwardness, mentioning the fact that I’m a learner (e.g. ‘Sorry, I’m still learning – could you repeat that?’ or similar) was helpful to ME because it reminded me that it didn’t matter if I was speaking like a three-year-old child, as long as I was understanding and being understood.
– Find someone you are comfortable with talking to one-to-one. I’ve had a number of speaking ‘buddies’ over the years with German and Spanish (slightly different in these cases because we would also switch to English so that they could practise in turn) and some partnerships have worked better than others based on shared interests, expectations and levels of correcting that went on. So I’d suggest putting some feelers out and finding someone who’d be willing to help you to practice regularly – and be clear to them what would be most helpful in terms of correction. Find a balance on the scale between from just letting you speak as much as possible, regardless of all mistakes (other than those that impede comprehension) to stopping you every time you make a mistake and explaining in detail what you did wrong. The former is the most useful in terms of building confidence, the latter is really not ideal in most circumstances. What I’ve found best is fairly ‘free-flowing’ conversation with occasional gentle corrections of mistakes that I frequently make.
– Talk with other learners. This can be a fantastic way to practice and gain confidence, because there is absolutely no pressure to express yourself elegantly!
– Also, a final (slightly unorthodox) tip: if arrangements allow, choose to meet up with your language buddy / group one evening in a pub and have yourself an alcoholic drink. Slight inebriation does wonders for making you care less about mistakes… But only in moderation: full intoxication just means you make no sense at all, in any language! 
Pob lwc – you can do it! 
), whatever you say in Welsh at this point really doesn’t have to come out perfectly or confidently, it just has to come out. When you feel yourself start to go into panic mode, take a deep breath and in your head count slowly back from 5 in Welsh… pump…pedwar…tri…dau…un… then at the same speed, start speaking but get some Welsh in there - anything, even if it’s mixed in with English as John suggested above.
) I even had a woman shout at me for not being able to hold a full coversation with her in Welsh which definitely didn’t help either.