Shifting a color to a web-safe color

Web safe colors have nothing to do with printing in the first place and even for display purposes "web safe" is simply an outdated concept fro ma time when web browsers could not display all types of images or colors. Therefore your actual issue likely simply boils down to a wrong print workflow, wrong print settings, lack of color management and so on. Based on your description my feeling is that CMYK is wrong here, anyway. It's more likely that whatever company is printing your T-shirt is simply printing from an RGB image using an inkjet printer and hence all your CMYK work is for nothing because without proper color management it simply gets misinterpreted/ used wrongly. In any case, you will have to be much more specific about what the requirements are and what you actually do. Could even be that whatever teal color you are trying to use cannot be recreated using a standard print process and additional steps and different workflows are required like actual silkscreen printing using a textile spot color. You have to clarify one way or the other.

Mylenium