Possible, with some drawbacks. The "standard" difference in head weights is roughly 8 grams. You could go with the lightest backweight available, but you could possibly lose a little forgiveness. Might just order a new TSR1 built to your specs so you know it's weighted properly.

You can already test the 40 g metal mesh from the TSR-1 in a TSR-2. The weight of the shaft is distributed along the length of the shaft so the swing weight won’t change much. A heavier grip can help balance it.
The woman in charge of development at Titleist in the TSi-2 series promotes a lighter shaft with a heavier -2 series head. Ball speed is a function of both club head speed and head mass. Her personal preference has been Speeder shafts. I have the TRS-1 5/7 woods with the metal mesh shafts. Have used the HZDOUS red shafts previously.
Reducing the head weight will affect MOI and likely change dispersion pattern. Try it first before changing weight