SrImad BhAgavatam i-4-25 empowers Women to study MahAbhAratam .
strI SUdra dvijabandhUnAm
trayI na Sruti gocarA
karma Sreyasi mUdhAnAm
SreyA evam bhaved iha
Iti bhAratam AkhyAnam
krupayA muninA krutam
As SrI VishNu SahasranAma is part of MahAbhAratam, women can recite it as Sloka pAtha after learning from a Guru. However, it may not be advisable for them to do anganyAsa, karanyAsa etc and recite the same as japa.
In my limited understanding, there is no bar on Women to recite SrI Vishnu SahasranAma as a Sloka pAtha without elaborate rituals covering anganYAsa, KaranyAsa , etc.