My question is : can I skip the 2nd 5532 and directly use the inverting amp (half of U1) to drive the output transformer (Edcor 1:1) ?
Yes. Actually the performance may be slightly inferior when the opamp operates at maximum gain and drives the xfmr, but the reduction of number of stages may very well compensate it.
I actually question the connection to the transformer via a 47r resistor.
At LF, the xfmr wants to see the smallest possible impedance, so a direct connection would be preferrable.
However, there's the risk of the cumulated offset voltages resulting in significant DC current in the primary, which would shift the magnetizing curve and generate distortion (2nd order).
Using a capacitor would solve the DC issue, but would result in a VLF response hump, that may cause intermodulation in the subsequent equipment. The usual fix is to use a huge capacitor, that would shift the hump under 3-4Hz.
Then there is the issue of stability, because the xfmr presents a significant shunt capacitance, which can be solved with inserting a ferrite bead.
The 47r is a cheap ans dirty fix for most of these issues except the VLF distortion.
Short of using a servo to attenuate offsets, a quite valid solution is to install a large capacitor in parallels with the 47r resistor.