The mechanically inclined would do this in a heartbeat, others not so quickly. Also, this is not something I have done personally but, I have read on this and other forums of others that have. With the time & correct tools it's not so bad.
Well, off the top of my head and assuming your wanting to do a simple swap, the good points of the Cobra tranny are the steel bearing retainer and the hardened input shaft at the front. Those are nice to have.
The not so good issues are the '96 GT's speedo/VSS are gear driven items where the '99 Cobra's is electronic sensor driven. (hence the digital odometer in the IP and no speedo gear on the output shaft) The Cobra's output shaft/tailshaft housing/driveshaft are of a different length which requires a slightly different frame cross member at the rear for the mount.
To even convert the Cobra trans to fit/work with yours, all the speedo, output shaft & tailshaft housing items from yours have to be transferred to the Cobra T-45. The speedo & tailshaft housing are easy to transfer as they are external. The transfer of the GT's output shaft requires a complete disassembly of your trans and the Cobra trans as the output shaft is assembled into the trans from the front. While your there, the replacement of synchro's, seals, bushings and any other worn parts are very possible due to the hard use some Cobras see.
At least I've given you an idea of some things to expect. There could be others. I would do some good research before attempting.
GT