Wouldn't those vibrational modes be damped by the mass rather than the weight of the ISS? Because the same goes for any other interaction between the ISS and its occupants, torquing down a bolt is no different from anything else. The biggest worry would be to upset the orientation of the entire ISS but I'm assuming that you are going to be tethered and/or connected to the ISS, if you didn't it would be you that spins rather than the ISS due to the difference in relative mass.