The shells are certainly different from rhd to lhd. The bathtub/bulkhead area is basically a mirror image, with the battery, fuse box and coil assembly swapping sides to allow for the pedal box to swap sides. The large hole for the pedal box is the obvious structural change, but the battery mounting plate and fuse box bracket are other sheetmetal differences. Also from memory, the hole the spline of the steering rack pokes into for connection to the steering column. So a few adjustments to make, but nothing insurmountable.
In terms of other differences, I don't believe the pedal assembly, steering column, or brake/clutch master cylinders are different, but the brake and clutch hydraulic pipes are. The wiring loom is sure to be different also, but this may be able to be 'reconfigured'. A pair of good rhd dip beam headlights could be tricky to find as well, but there are ways around this. I think the door mirror is non handed so can just be swapped over.
Luckily Alfa didn't bother swapping the boot release to the right side so you needn't either.
As an aside, why do you want to do this conversion?