In the office I work in, filled to the gills with Japanese nationals (I am in Japan after all), no one says "shine-toe." A quick poll by the Mandylion Polling Agency found a 100% response to the "Shin-toe" option as being correct. "Shine-to" drew responses of "ちょっと変ね..." (that is a big off...).
But you know what they say about polls.