https://ja.wikipedia.org/wiki/卑語#日本語における卑語
swear word: a word of a kind used to express anger or other strong emotion and regarded as coarse, blasphemous, or otherwise unacceptable in polite or formal speech.

I think it is a separate sense but the JEs and smaller kokugos don't mention it. Probably safe to ignore.
I don't think "profanity" or "swear word" should lead. That's a specific type of vulgarity. None of the Japanese examples on the 卑語 Wikipedia article are swear words. 
鄙語 is in all the kokugos and isn't 旧字体.

@@ -9 +9 @@
-<ke_inf>&sK;</ke_inf>
+<ke_inf>&rK;</ke_inf>
@@ -16,3 +16 @@
-<xref type="see" seq="1482760">鄙言</xref>
-<gloss>profanity</gloss>
-<gloss>swear words</gloss>
+<gloss>vulgar word</gloss>
@@ -21 +19,2 @@
-<gloss>language used in rural areas</gloss>
+<gloss>profanity</gloss>
+<gloss>swear word</gloss>

JEs, kokugos

Despite what some kokugos have, I think it's only one sense.

@@ -9 +9 @@
-<ke_inf>&oK;</ke_inf>
+<ke_inf>&sK;</ke_inf>
@@ -15,0 +16 @@
+<xref type="see" seq="1482760">鄙言</xref>
@@ -18,6 +18,0 @@
-</sense>
-<sense>
-<pos>&n;</pos>
-<xref type="see" seq="1482760">鄙言</xref>
-<misc>&obs;</misc>
-<gloss>language used in rural areas</gloss>
@@ -25,0 +21 @@
+<gloss>language used in rural areas</gloss>

sanoku:下品な内容の言葉

Google: "卑語"　"swear words" (lots)

卑語 is the wiki xref for "profanity"
https://ja.wikipedia.org/wiki/卑語
卑語（ひご、英語: Swear Words）とは、


卑語	3575	97.8%
鄙語	82	2.2%

nikk 卑語:
〘名〙 いなかのことば。また、世俗のことば。鄙言。
nikk: 鄙言:
 田舎の言葉。また、世俗の言葉。鄙語。

Even among the 64 yourei examples, a bunch are discussions of foreigners.  They generally look like uses of "profanity" to me...
https://yourei.jp/卑語

I've commented on "vulgar" meaning "of the masses" here before.  It will be misunderstood by most users (and is ambiguous in any case).

@@ -8,0 +9 @@
+<ke_inf>&oK;</ke_inf>
@@ -14,0 +16,8 @@
+<gloss>profanity</gloss>
+<gloss>swear words</gloss>
+</sense>
+<sense>
+<pos>&n;</pos>
+<xref type="see" seq="1482760">鄙言</xref>
+<misc>&obs;</misc>
+<gloss>language used in rural areas</gloss>