Can a Laser be rigged using only the top of the mast?

It's not at all clear what you are asking, but if you mean, "Can a Laser be rigged without the bottom section of the mast?", the short answer is no. If you seek more info perhaps you can further explain your question.
I understand your question now but I'd still say no. If you found a lateen rig (that's what's on a Sunfish) you could adapt it to fit on a Laser but I really think that's not the best thing to do. You would no longer have a Laser, though if you didn't remove any of the Laser hardware you could switch between the rigs. But I don't know if the Sunfish mast fits in a Laser hull.

You could:

1) look for a Sunfish and sell your Laser, which I guess you are trying to do,
2) learn some of the "tricks" to make stepping the mast easier, or
3) have a zippered sleeve put in your sail or a new sail and add a halyard.

I favor #3 as it doesn't wreck your boat. Your could buy a practice sail from some place like Intensity Sails and pay a sail maker to add the sleeve. That way you step just the mast (without sail) and raise the sail with the halyard as is done with some similarly sized boats like a Zuma. That's of course not class legal but you can keep the original sail if class legality is important to you and even if it isn't, this option will retain the value of your boat.
Put the lower in the boat, use that as leverage to tilt the whole thing and insert the upper. You could head to your sail maker and have a zipper installed in the luff tube, that would make it easier to get the sail on and off.