I only have about 8 more weeks of school to go before Im finished grade 12! In the next few weeks I really want to talk the careers teacher about organising an electrician apprenticeship for soon after I leave. I need to give her a resume tho and Im not really sure what name to put on it. Would I get into trouble for putting a preferred name and no legal name on it?

The other problem is my only referees know me as my legal name and female  If the apprenticeship people call my referees and ask about me using my preferred name, my referees will have no idea who they are talking about. That might be an issue  Then again, I am stealth at school and if I put my legal name on the resume, it would mean coming out to the teacher (but that shouldnt really matter?). I really want to start working as male next year, and I dont want to stuff it up. I tried to avoid doing this earlier cause I wasnt sure what to do. But I really need to do something now.

Would it be best to just do the name as... Legal Name 'Preferred Name' Last Name? and explain it all later? Also can they not hire me because I look much younger than I am? I dont know how people would feel have a "12 year old" doing electrical work in their house 

I don't know where you live, but here in Canada the importance of having the legal name is for two reasons, and the primary reason is to do a background check. If you're not giving them your legal name, which they need in order to do the background check, then they'll likely find out and not hire you/take back the job offer. The other thing is for pay check reasons, though that isn't as important as the background check/making sure you are who you say you are, you don't have a criminal record, haven't had cases of gross misconduct at jobs in the past etc.

On the other hand, it's not like they are filling out the backcheck form for you based on the resume, so if you put your chosen name on the resume, you just have to be sure to put the legal name as the primary name on the backcheck form, and just explain to them at that point that your legal name is X, but you prefer to use Y.

You'd also have to make yourself aware of whether or not the programme/company/place where you live has laws to protect trans people from discrimination in the work place, or that the company has a functioning diversity programme in place. Either way, you'll have to at least come out to your employer, though neither you nor the employer need tell other employees if you want to remain stealth.

In all these types of situations, I always tend to think its a good idea to talk to an lgbt councilor who's aware of the legal aspects/what your rights are, before proceeding and making assumptions that might get you into trouble where you live.

And of course, you could circumvent all of this by changing your name legally

If you're going into a union program, check and see that the requirements are the same for men and women.  They tend not to be, ours is carry 50lbs for girls, 75lbs for boys.  And electrical stuff is heavy, I wouldn't doubt that they have up to a 100 lbs limit.

A bit of a tangent:

Yes, I've seen weight lift requirement for anywhere from 25, 35, 50, 70, 75, 100 pounds.

I passed the UPS 70 pound requirement.
The recruiter looked at me and said, "Well, if you need to lift 70 pounds you can use a handtruck."

Our primary electrical cables are 2 inches of pure copper in diameter, fifty foot lengths, usually tied together in groups of five in hods.  Heavy as ->-bleeped-<-.