A non-cementatious grout would be even more fun. There, you'd want fantastic site-to-exterior ventilation (explosion proof fan and flexible ducting) and use acetone or xylol to dissolve the cured epoxy or vinyl grout.
I once had to curtain off adjacent spaces with plastic thoroughly taped down, then open an exterior door. I used a rubber trash can with the bottom cut off and a large box fan blowing air into an opening in the plastic to provide positive ventilation, forcing clean air into the space to displace the fumes. I did not have an explosion proof fan and did not feel like burning up the house and what's left of my hair.
Use an appropriate respirator, no matter what you do. It can be a big deal.