You pose a very complex question! So, let's start digging into it.
First, the simple elimination....if you don't want to be drowsy, don't take Dramamine. And barring some other unspoken malady or symptom, that may be the only exclusion.
So what are you left with? Bonine is acceptable to use in hypertensive patients, with a relatively small incidence of causing drowsiness. Scopolamine patches do not carry any precautions for people with high blood pressure. Ginger capsules are a nutirnional supplement and have no real effect on high blood pressure therapy. And the non-pharmacological intervention, SeaBands, can be safely used, though their effectiveness remains questionable, at best.
I hope that I provided the answers that you needed, Sandy! Happy cruising!