Every time I glide the shaver over my skin, I really do get a sm~ooth feeling.

Literal

Skin [on-に] shaver [object-を] glide [every-time-度に], certainly smoo~th [attributive-な] feeling [subject-が] do.

Product-review register. ~度に ('every time ~ happens') is formed from 度 ('occasion, time') plus に. 滑らか~ uses the extended vowel mark as an emphatic device ('smoo~oth'), common in informal writing and advertising. 感じがする ('to get the sensation/feeling that ~') is the idiomatic way to report a perception. 滑らす is the transitive 'to glide (something),' contrasted with intransitive 滑る.