Is there any way to implement Fuzzy search with SearchStringModel technique in sitecore?
No, not from what I see in the API.
While reviewing the class
Sitecore.ContentSearch.Utilities.QueryBuilder, Sitecore.ContentSearch you can see that there is no place with a conversion for "Like".
In addition, while reviewing the class
Sitecore.ContentSearch.PredefinedQueryAttribute, Sitecore.ContentSearch.Linq you can see that there is a reference to "Like" but requires the code to make use of
Expression Trees are a beast and looks like Sitecore did not expect the fuzzy search to be used from the UI.