The simple halachic principle is that a Sepharadi should generally be following the opinion of Maran Hashulchan Aruch as the bnei edot hamizrach have accepted his teachings as the 'majority' halachic authority as Rav Ovadia puts it. In a case of a mitzvah deoraita, it would be correct for you to follow our 'chief halachic authority' as the Torah says we should do.
For mitzvot derabannan, you are 100% allowed to be mekeil and follow other opinions, notably the Ashkenazi poskim. Obviously, following Maran is preferred but it's not necessary at all.
And I say this is the general rule because there are quite a few exceptions with very good reasons. For example, Safek berachot lehakel does work against Maran according to Rav Ovadia who notes most exceptions where we don't follow Maran and follow/take into account other poskim e.g. Arizal, Ashkenazim and the reason why. (I.e. Minhag avotenu, biyadenu?)
Referring specifically to your shaver case, Maran obviously doesn't mention this modern day case. It's much preferable to follow Rav Ovadia as in many cases he applies modern day cases to Maran Hashulchan Aruch so it's best to read his teshuvot to see his source and reasonings. After all, shaving is mideoraita and we should follow our own rabbis (gedolim) as the Torah has commanded us even if he doesn't apply Maran to our modern times.
However meikar Hadin there does seem to be room to be mekeil to follow the opinion of contemporary Ashkenazic poskim provided that they have strong foundations for how they rule which I'm sure they do.