actually other than filling out the employment part which includes the company name and business address in application form for the course they won't ask you to show proof that you are actually working for that company so you can still go ahead and take that course.
The reason why I think they would want you to be employed in the first place
The courses are already discounted by NTUC and further subsidized by citrep, application for citrep assistance/reimbursement would require to show proof of your employment I think and in the event you are not employed it will be to your disadvantage as you can claim back 40-50% of paid course fees in some cases thru citrep which is quite substantial amt.
For your case I think if you want to avoid this problem 2 things you can do.
1) ITE courses, they do have a continuing education program on a pretty wide spectrum of IT/electrical/engineering short courses. Quite cheap also.
2) See your minister at "meet the people session" to raise your problems if all else fails, they are there to help you and especially during this period they even more keen to help you

other than writing out a blank cheaque to you, they can help you in ways that you cannot imagine possible by writing a simple letter of recommendation perhaps? For your case since you are not asking for a handout ... it will be in the bag.