Very carefully.
No nukes because the Gulf is mud geology, and the mud is full of Methane Hydrates. It would produce and ignite the largest gas bubble ever, blowing a big hole.
Even the relief well is dangerous. The idea is pump in mud, Specific Gravity of 2, but the water was nothing to blow out. Just like it blew out the top kill, it can blow out bottom kill. I figured several million pounds of force coming out of the pipe, and the mass in motion of over three miles of oil.
MxV=I, and I is a really big number.
The hope is that the mud is a brake that slowly slows the flow and lowers I, but just for starters it will double pressure in the casing.
For it to work the mud must replace the oil, and the oil is in motion. All of that force will be on the bottom of the mud where the relief well intersects.
It will not be a tight joint, they are drilling blind into a pipe miles down, cutting a hole in the casing that confines it.
Before the blowout the pressure of the non moving oil was confined by mud to the surface, now with a mile missing.
The dangers are, would 8,000 foot of mud stop it? it has to stop before it can be cemented.
Will the added presure of mud in the casing just split the casing? There are already reports of oil coming out of the sea bed around the casing.
Making holes in the casing leaves the area around it an open path to the surface. the hole is larger than the casing, all the way down.
I can be mudded, cemented, and have a blowout all around the pipe.
With nothing much holding it in place the whole casing can be spit out of the hole.
Outer casings are not used for production because the tools go up and down, bits and stem move about in the hole, and have huge mass. Casings get holes.
The production pipe was set, most likely 12" inside, and that is what the cement joint was trying to do, fill the space between the two pipes.
So if the casing is cut, mudded, cemented, there will still be a production pipe flowing. it reaches from the sea bed all the way down. Drilling through it, it will just drop, all your mud will be above, so it will still have an open path.
Mud has weight when it is sitting still, a solid tube of mud moving as fast as the oil will just flow up and out. To replace the oil it has to have more force, and that just where the oil will concentrate all of it's force. That just happens to be the place where the casing was cut to inject the mud.
This could get much worse.