Alteration from 如何しい (ikagashii), itself derived from 如何 (ikaga, “how; uncertainly”) +‎ しい (-shii, adjectivizing suffix).

The sound shift from /ikaɡaɕiː/ to /ikaɡawaɕiː/ was probably influenced by the medial /wa/ in roughly synonymous adjective 疑わしい (utagawashii).

• (Tokyo) いかがわしい (Nakadaka – )
• IPA^(key):

如何(いかが)わしい • (ikagawashii) ^{←いかがはしい (ikagafasii)?}-i (adverbial 如何(いかが)わしく (ikagawashiku))

1. unreliable, doubtful, uncertain

   あのがたのきている橋(はし)は如何(いかが)わしい。

   Ano gata no kiteiru hashi wa ikagawashii.

   That rickety bridge is doubtful.

2. questionable, dubious, suspicious
   • 濃紅葉小倉色紙 (Koi Momiji Ogura no Shikishi), kabuki play; 1816:

     斯(か)やうな儀(ぎ)を御(ご)諫(かん)言(げん)申(もう)し上(あ)げられぬは如何(いかが)はしう存(ぞん)じまする…

     kayau na gi o go-kangen mōshiagerarenu wa ikagahashiu zonjimasuru…

     I think it's suspicious that he can't admonish this kind of happening...

3. indecent, licentious, obscene

   如何(いかが)わしい意(い)図(と)、如何(いかが)わしい話(はなし)

   ikagawashii ito, ikagawashii hanashi

   indecent intent, an obscene story

4. disreputable, dishonest, shady

   如何(いかが)わしい商(しょう)売(ばい)

   ikagawashii shōbai

   dishonest dealings, disreputable business

• 如何わしい implies something that cannot be trusted, or that may be immoral.
• 疑(うたが)わしい (utagawashii) implies something for which the true nature or quality isn't known, but that may be good or may be bad.
• 怪(あや)しい (ayashii) implies something for which the true nature isn't known, and this uncertainty is a bad thing.
• 訝(いぶか)しい (ibukashii) implies something for which the true nature isn't known, and this uncertainty causes one to be curious.
• 胡(う)散(さん)臭(くさ)い (usankusai) implies something suspicious that draws attention.

• (unreliable, uncertain): 信用できない: 信(しん)用(よう) (shin'yō) (“confidence, faith”) + 出(で)来(き)ない (dekinai) (“cannot”); 不(ふ)確(かく)実(じつ) (fukakujitsu)
• (questionable, dubious): 疑(うたが)わしい (utagawashii); 怪(あや)しい (ayashii); 胡(う)散(さん)臭(くさ)い (usankusai); 訝(いぶか)しい (ibukashii)
• (indecent, obscene): 助(すけ)平(べい) (sukebei); 下(げ)品(ひん) (gehin); 卑(ひ)猥(わい) (hiwai); 淫(みだ)ら (midara)
• (shady, sly): いんちき (inchiki); 怪(あや)しげ (ayashige); 胡(う)散(さん)臭(くさ)い (usankusai)