Sometimes I don’t feel comfortable with the sanitary conditions of a washing cup. More than sometimes. At work the non-Jewish workers sometimes use the washing cup for cleaning and at home my wife uses it to dip int he bathtub and wash the kids’ hair. The nature of these washing cups in general is not very sanitary and they don’t lend themselves to be cleaned thoroughly. I was just washing at work on bread and there was something floating in the water from residue from the cup. I rinsed it out and filled it again and used it but I feel disgusting about it. I was wondering if I could have washed with a reviis on each hand (so it would be okay if my hands would remain wet according to what I remember from the MIshna Brurah) and then, either before or after drying them, to wash again with soap under the faucet before making Hamotzie? Even if there is some room for flexibility in washing my hands again, would it be considered a hefsek between the netila and Hamotzie? Would a better option be to use a disposable plastic cup to wash, which would avoid making me feel disgusted altogether?
From your question it sounds like you are extremely sensitive to cleanliness, and it bothers you if the cup was used for something else besides netilas yodayim. Although it is doing something in between the washing and the bracha, however it can is still be considered part of the washing process. Therefore it is beter for you to wash your hands with soap etc. than to use the plastic cup.
As a side point it would be good for you to try and train yourself not to be so sensitive, as the gemora says, (“shlosha chayihem einom chayim… istonis”) that an overly sensitive person person’s life is miserable. Therefore maybe it would be worthwhile that you use the regular washing cup once a week, to get used to desensitizing yourself.