It is true that Korean ㅎ has a very wide range of allophones, more so than the English h. So your perception that the ㅎ sounds "different" in the syllable 협 is not just based on an error.
This is the concept of allophones, and Korean ㅎ has a very large number of them. From Shin, Kiaer, Cha's 2012 seminal work, The Sounds of Korean:
Major allophones: /ç/ before /j, i/ in word-initial position
/x/ before /ɯ/ in word-initial position
/ɸʷ/ before /u, o/ in word-initial position
/h/ before all other vowels in word-initial position
/ʝ, ɣ, β, ɦ/ voiced counterparts in word-medial position
The fusion of the /h/ and the /j/ (the sound) in Korean 협 results in the voiceless palatal fricative [ç], which is quite common in British and Australian English (hue, pronounced [çʉː]), and also attested in American English. If you've studied German before, it is the ich-Laut of standard Hochdeutsch.
So 협 in IPA follows the allophonic change: /hjʌp/ -> [çʌ̹p̚]. Although it is most naturally pronounced this way, most English-speakers will be able to get away with the /hj/ being pronounced more like in English.
Note also that it may be affected by voicing if in the middle of a word, e.g. in the word 타협 "compromise".