mirceme,
If you have any luck with the chisel routine, than you're more adept at using one than I am. Let me make two other suggestions.
Having recently removed and rebuilt the ignition switch in my 74.5 MGB-GT, I have a pretty good idea about how to remove it.
If you have a Dremel tool, or can borrow one from a friend, than you have the best tool for the job.
Based upon your description, you have removed the steering column covers to gain access to the switch. The "headless" bolts are referred to as shear bolts like Gavin mentioned, but I believe they were used less for anti-theft as they were to facilitate faster assembly. Since the heads shear off at a predetermined torque, they could be installed without having to use a torque wrench. Installers just kept turning untill the head twisted off.
Back to your question...
The bolts are made of aluminum or some other soft metal, and cut rather easily. Install a cutting disc in the Dremel tool and carefully cut a straight slot all the way across the top of each bolt. If you make the cut with a new disc, and cut as deep as you can without cutting the flange surrounding the bolt, you should should be okay.
Using a flat blade screwdriver with a blade width as close to the bolt diameter as you can find, unscrew the bolts.
I used this technique about three weeks ago, and the bolts screwed out easily.
YOU MIGHT NOT HAVE TO REMOVE THE SWITCH HOUSING
If you have a key that fits the "bad" ignition switch, and it still functions with respect to locking and unlocking the steering column, then you might not have to remove the original switch housing.
What you're calling the switch is made up of three basic components: 1- a keyed cylinder (where the key goes), 2- the housing (mounted with the shear bolts), 3- the actual electrical switch (black plastic piece with the wires soldered to it).
If your replacement switch is identical to the original, then you can save yourself some time this way.
The electrical portion of the switch is obviously at the opposite end from the key. Looking at your original equipment switch housing, you'll see a small, number 1 phillip's head screw close to the edge of the housing, at the switch end. Removing this screw will allow you to slide the electrical portion (the actual switch) out of the housing.
The connection between the switch and the ignition key cylinder is a t-shaped male/female interface that will allow the switch to be removed in this manner. At most, you might have to insert the key and give it a little twist back and forth while pulling the switch away from the housing.
With the original switch removed, you can install the new switch just as easily by reversing the proceedure.
Of course, this is based upon your replacement being constructed the same way as the original.
You'll find that the switch's wire harness is taped to the steering column with a wrap or two of black electrical tape, and that the connection is beneath the edge of the dashboard to the left of the column. The connector separates easily, just look twice at the little plastic "levers" on each side to make sure you're releasing them instead of holding them on tighter.
Hope this helps,
Mike