Without a commonly accepted writing system for American Sign Language (ASL), Deaf or Hard of Hearing (DHH) ASL signers who wish to express opinions or ask questions online must post a video of their signing, if they prefer not to use written English, a language in which they may feel less proficient. Since the face conveys essential linguistic meaning, the face cannot simply be removed from the video in order to preserve anonymity. Thus, DHH ASL signers cannot easily discuss sensitive, personal, or controversial topics in their primary language, limiting engagement in online debate or inquiries about health or legal issues. We explored several recent attempts to address this problem through development of "face swap"technologies to automatically disguise the face in videos while preserving essential facial expressions and natural human appearance. We presented several prototypes to DHH ASL signers (N=16) and examined their interests in and requirements for such technology. After viewing transformed videos of other signers and of themselves, participants evaluated the understandability, naturalness of appearance, and degree of anonymity protection of these technologies. Our study revealed users' perception of key trade-offs among these three dimensions, factors that contribute to each, and their views on transformation options enabled by this technology, for use in various contexts. Our findings guide future designers of this technology and inform selection of applications and design features.