Firstly, even if the reference to "right" is to the right arm as part of an oath, I'm not sure how one could conclude they raised the arm. Maybe they just held it sideways or against their body or some such.
Most Hebrew commentaries (Radak, Ibn Ezra, Metsudat David) explain "right" to be metaphorical - the right being typically stronger than the left, represents a person's power, strength and conviction. The translation "right hand" shouldn't be understood as having any relation to oaths according to these explanations. The first clause therefore refers to these people's words whereas the second refers to their actions.
This metaphor recurs throughout all of scripture. See Psalms 118:15-16 for example.
Interestingly there is a very relevant verse in Isaiah 62:8 where "God swears with his right and the arm of his strength". For these explanations this is proof not that the "right" is used in taking an oath (although that would be a very tempting first impression), but rather that "right" is a reference to strength (as supported by the end of the clause). The verse comes to say that God wears by His strength and might that your food won't be given to your enemies etc. See the verse in context.
Interestingly the masoretic Aramaic translation translates "right" as אוריתה - law or teaching. This explanation is also that "right" is metaphorical, but referring to a more spiritual strength and conviction. Referring more to the evil-doers beliefs and moral code than to their actions. Again, I emphasise that "right" doesn't correlate to oath-taking.
That covers most of the verse exegesis. Looking into Hebrew tradition, we see that swearing an oath in Hebraic tradition is almost purely a verbal thing (see Maimonidies Laws of Oaths, chapter 2. This doesn't exclude however the judge's oath, see chapter 11, during which there was a religious item held, presumably the basis for modern-day swearing on the bible, although that isn't the topic here). Scripture's description of oaths is often things people say - note how most verses are of the form "and he swore ... saying ...". Genesis 24 being an exception, although that seems to be related to the handshake concept we are about to discuss, see the Ibn Ezra's explanation of verse 2, and the Rashbam who says this is equivalent to a handshake.
There is some debate as to the status of a handshake. It is not mentioned in talmudic literature, however medieval codifiers disagreed as to its legal status. There are two separate uses for a handshake - one as an act of purchase (in talmudic law a transaction became official with some physical act - not relevant to our discussion) and one as an act of taking oath. Opinions vary from a covenant (considered more binding than an oath) to not even a valid oath. In any event, there does appear to be some (albeit late and not agreed upon) reference to the handshake as a form of oath, and this is what commentators (Divrei Ya'akov for example) believe Rashi is explaining in his commentary (the only Hebrew commentary I found that seems to consider "right" something other than the aforementioned) on the verse in question when he writes that the people would "come to make an oath with their right hand" - not raising their hand to swear since in Hebrew law that has no validity whatsoever, but rather swear an oath (i.e. enter into an agreement) with a handshake.
In any event, it seems highly unlikely that the reference "right" has anything to do with raising one's right arm to swear an oath.
For another interesting and relevant biblical example see Daniel 12:7, but compare it to Chronicles II 6:12-13 and Exodus 9:29,33.