Is it possible to have the Eurasian/mixed look by doing only double eyelid surgery but without removing my epicanthal folds?

If you do not have significant skin in the inner corner, then a medial or inner epi is not necessary. The removal of the inner skin is mainly to enhance the natural curvature of the double eyelid fold.

In general, when medial epicanthoplasty is performed in addition to Asian eyelid surgery, the eyes may perhaps appear more "Eurasian". However, in my opinion, neither Asian eyelid surgery nor epicanthoplasty should be performed to achieve an "Eurasian look". Instead, these procedures should be done to enhance the aesthetics of the existing eyes.