Assuming you're talking about the right hand side, you're not going to get away without welding the downpipe unfortunately. If memory serves, it is curved right up until the point where it goes in to the flexi, so no straight section long enough to fit a slip joint.
What may be more feasible is to get hold of a pair of 3-bolt flanges (ideally get a left downpipe gasket copied and laser-cut in 8 or 10mm steel) which you can then weld on to the right hand downpipe before the flexi. If you get the flange sized so that it fits over the downpipe you can then mig it from the inside, which is much easier to get to. Then, continue with your plan but also weld a flange on to the new flexi, essentially replicating the left hand side.
I do have some 3.7 downpipes cut at the flexis in the workshop. If I remember tomorrow I'll grab a pic of them
