Direct answer
SR626SW/377 and LR626/AG4 both measure 6.8 × 2.6 mm. The watch cell is silver oxide at 1.55 V with an SW low-drain designation; LR626 is alkaline at 1.5 V with a general-purpose profile.
Both are 6.8 mm in diameter; heights are 2.6 mm and 2.6 mm. The 6.8 × 2.6 mm envelope matches, but the electrical families do not: Silver oxide / zinc at 1.55 V nominal versus Alkaline manganese dioxide / zinc at 1.5 V nominal. Physical fit is not equivalence.
Do not infer acceptability from fit alone. The device maker’s complete code and current instructions remain authoritative.