Your assumption that there is a halachic need for niguv (drying of the hands) is basically correct, but the underlying reason affects its requirements.
One of the rationales that Tosafot[1] gives for the practice of making the beracha on netilat yadayim only after the washing has taken place[2] is that netilat yadayim is not completed until the niguv, which follows the beracha, is done. This seems to give a halachic status to niguv, which Tosafot justifies by citing the gemara,[3] which states, “Eating without first drying the hands is like eating tamei (impure) bread.”
In what way does the bread become impure because one washed but did not dry his hands? One suggestion involves the halacha that the water one uses for netilat yadayim can become tamei after the first washing, and steps need to be taken to remove it from the hands. Although the basic solution is to wash the hands a second time, some poskim believe that niguv is a final part of the removal process.[4]
Rashi comments on the aforementioned gemara that the problem with not drying hands is mi’us (unsightliness), which can also be called tamei. He apparently means to say that niguv is a matter of manners, as wet hands make bread soggy. It is difficult, though, to say that mi’us is the only issue. The tosefta[5] says that niguv is required only after netilat yadayim, not tevillat yadayim.[6] If the issue is tumah, the distinction is understandable, since after a single immersion, all the water is pure. However, regarding mi’us, why should there be a difference between whether moisture remains on the hands from washing or from immersing? (The Taz[7] rejects the possibility that the gemara disagrees with the tosefta).
Therefore, a third explanation is suggested,[8] which includes elements of the first two. The heart of the problem is mi’us, due to which the Rabbis instituted that the procedure of netilat yadayim would be incomplete until niguv, which solves mi’us, is done. However, in regard to tevillat yadayim, which is a throwback to the Torah laws of tevilla, the need for niguv was not formalized.
There is a major difference between the approaches of removing tumah and of a formal requirement related to mi’us. It arises when one does netilat yadayim with at least a revi’it (3-4 ounces) of water for the first washing. The Shulchan Aruch[9] says that since in that case there is sufficient water to wash away the impure water, niguv is unnecessary. The Maharshal,[10] in contrast, maintains that since there is an issue of mi’us, niguv is required. The latter approach is the prevalent one.[11] Therefore, even after netilat yadayim with a lot of water (which is now commonplace), niguv is needed.
The Levush[12] makes a claim that is pertinent to our question. He says that the tosefta never denied a need for dry hands after immersing, but meant only that the drying need not be done in a formal, halachically effective way by using something absorbent. Consequently, after tevilla, when there is no problem of tamei water, one can allow the hands to dry naturally so as to avoid mi’us. In contrast, in order to remove tamei water after netila, an absorbent material must be used. Several poskim accept the Levush’s stringency.[13]
In all probability, using an electric dryer is considered a means of speeding up the process of hands drying naturally and would not suffice according to the Levush. However, if one used a revi’it of water (as is most common) for the first washing, such that the issue is only one of mi’us, the Levush’s concern does not apply, and even the Levush, and presumably the Maharshal, would agree that using an electric dryer is fine.[14]