Can it be said that proteins determine phenotypic traits?
Yep, that is correct in general. However, sometimes proteins indirectly determine phenotype. For example, the skin colour is dependent on melanin (not a protein) but the melanin producing cells work because of proteins. Further, melanin production is also controlled by proteins. Thus, skin colour is not DIRECTLY determined by proteins but because proteins produce the pigment melanin, proteins are ultimately the reason behind our skin colour phenotype.