Social distancing may force people to restrict social touch practices. Our survey (N=136) highlighted substantial social touch breakdowns during the COVID-19 pandemic for semi-intimate relationships (e.g., friends, colleagues), with handshakes being the most reduced, and frustrations at having to re-establish social touch habits. We then designed SansTouch, a multi-modal hand sleeve used together along with a smartphone to enable mediated hand-to-hand interactions such as handshakes or holding hands. To invoke the mediated touch, users synchronously mimic the hand position as in real life while holding SansTouch. Users can feel the touch sensation in real time without touching. Participants from our observational study (N=12) quickly adopted the hand-to-hand interactions of SansTouch for exchanging greetings face-to-face with colleagues and reported stronger preferences towards using SansTouch as opposed to mid-air gestures (e.g., waving). We discuss design implications, including the trade-offs of multi-modality for touch devices in face-to-face communication.