Keeping your educational background and work experience in mind, my suggestion is to first try and leverage your core competency of computer engineering. There are two reasons I suggest this. First, it is a niche arena and so there could be greater chances of finding suitable openings and secondly there is a higher probability of you doing exceedingly well in that field because of your inherent educational background and work experience.
Coming to training, it pre supposes that your communication skills are excellent but more importantly requires a different domain expertise, especially if you hope to go into soft skills or management related training. Training exclusively for the computer related domain would narrow your options drastically too.
Finally you have to decide which area interests you, excites you and what is it that you are really passionate about. If your passionate about anything you can be sure you will find ways and means to surmount all inhibitions, apprehensions, obstacles and failures and live what you dream.
From India, Mumbai
Like B.Jacob mentioned, first & foremost figure-out the following aspects:
1] What's your core INTEREST--training or testing?
2] Where do your core STRENGTHS/CAPABILITIES lie--in training or testing?
In short, do a SWOT analysis of the various options you see for yourself & you will have the answer for yourself.
There's, however, one fallacy in what you mentioned: '.............there are lots of openings in Testing'.
Pl note that ANY & EVERY field needs experience for any company to consider that individual's application. With just a training course, it would be tough for you get any worthwhile Testing job opportunity, unless it's for freshers.
All the Best.
From India, Hyderabad