Beyond the goals of increasing quality and productivity levels or reducing cost, time and cognitive efforts, translation technologies are now designed, more than ever, to be as enjoyable and easy to use and learn as possible. In order to achieve the latter, translation software providers try to account for different end user profiles by designing, among others, cross-device, cross-platform solutions and multimodal interfaces. However, and despite the progress made to date in the area of Human-Computer Interaction (HCI), recent research work has suggested that leading desktop-based CAT tool providers fail to consider the particular needs of blind translators when developing their software. As the translator-tool interaction is based on keyboard-only input and text to-speech or text-to-braille output, common tasks such as consulting the translation suggestion's provenance can be extremely time consuming or even impossible for screen reader users unless they receive sighted assistance. Taking into account the conclusions drawn in prior research work about the low level of accessibility featured by the most popular desktop-based CAT tools, we conducted a study to explore the potential of web-based CAT tools as a more suitable solution for blind translators. Our study was grounded on the belief that web development techniques are more standardised and, therefore, a higher level of accessibility can be achieved. We followed a classic usability evaluation approach, where a cohort of blind translators were requested (i) to conduct a simple post-editing exercise using two different MT-integrated online CAT tools, and (ii) to provide information about their interaction with the software. More specifically, translators were asked to report any issues encountered while trying to perform the post-editing exercise via a validated frustration experience form, used in prior work for HCI studies of similar nature. Once the interaction finished, participants completed a survey, inspired by the Computer System Usability Questionnaire (CSUQ), including questions about their overall user experience with the software. The two tools chosen were the only ones among a selection of six popular web-based post-editing environments which, during a pre-test, met the basic accessibility requirements needed for the study to be feasible. Findings indicate that, while usability scores are not extremely low, slight changes in the tools tested would be needed for screen reader users to be able to perform a translation job autonomously and efficiently. Data gathered has contributed not only to identify current challenges faced by blind translators when using the two tools evaluated, but also to provide important insights into which general recommendations could be followed by translation technology providers to adopt an accessible design approach when developing their software. Overall, our study suggests that accessibility awareness is still low, and that further research and development is needed in our industry to guarantee equal opportunities for all in the translation market.