What is the risk of removing a feature with low correlation...?
Variable selection in linear regression is based on partial correlations, not zero order correlations. The partial correlation is the one resulting after a conditioning variable effect is removed from both X and Y. 

While a variable may be non highly correlated with Y, it may be highly correlated with an X variable in such a way that the X variable after being partialled out of the conditioning effect becomes highly significant. 

This effect is known as suppression among other names. 
HTH