Just an FYI, those are still Latin Alphabet characters. They are just give Diacritics to denote a different sound that the letter represents. Considering that the language you're writing for is Modern English, it would probably be best to go with the second version, since your diacritics are not common and most English readers won't know how to pronounce them.
The reason Diacritics exist is that the Latin Alphabet may not have been developed for a language that uses it and different languages have different sounds. For example, the Hawaiian, Navajo, and Quechan languages were not written language until westerners had contact with the Hawaiians', Navajo, and Inca respectively. The official writing script for each uses Latin, but sounds exist in a written form that may not be indicatively pronounce. For example, the Navajo call themselves "Diné" (The people). Although the word looks like it should be pronounced like the English word "dine" (as in "to eat") but the "e" is pronounced as a hard "e", like how Canadians end all of their questions, eh? But it's not nearly the same sound... it's more like the sound in "hay"... so to denote the "e" does not represent the same sound, the diacritic is added to denote to readers it's not pronounced like you would read the word.
Again, because Icelandic (also uses the Latin Alphabet... but with heavy use of diacritics because it's not a language that developed with Latin influences) the diacritics denote sounds that the letters don't ordinary represent in that spelling. But since your audience is likely to not know the pronunciation rules do to limited exposure, they might have trouble with properly pronouncing the character, especially considering you're only doing an approximation to modern Icelandic, which is several centuries of linguistic drift from the old Norse parent, which has no guarantee of being remotely close. Consider that some linguistics believe that the best approximation of what William Shakespeare plays would have sounded like is to do Hamlet... in a U.S. Southern accent instead of the Queen's. Specifically, a Tidewater accent (common in and around the state of Maryland. Although hanging a "hon" on "To be or not to be, that is the question" might be advised against. For the record, I always read Romeo and Juliet with the former in a surfer accent and the latter in a valley girl... but that's just me trying to inject humor to stave off the boredom.).
Point is, many languages develop by drifts in pronunciation becoming so distant, the parent language can't understand the child any more (Romance Languages are languages that are basically exaggerated accents of Latin from that area of the Roman Empire.). Several modern languages are now going through the process of getting regional distinctions that are bordering this (America and Great Britain are often said to be two nations separated by a common language. Latin America Spanish and European Spanish are so distant that many films are dubbed into separate regional Spanish depending on the market. Quebec French and Brazilian Portuguese are also very different from their European counterparts. Even Pennsylvania Dutch is difficult for someone who learns European German.).