Within Germanic, it's only the North and West Germanic languages that have /y/ (and /œ æ/, which you didn't ask about, but which owe their existence to the same umlaut phenomenon); Gothic lacks these sounds and they're accordingly not reconstructed for Proto-Germanic. It's possible that Northwest Germanic languages got these sounds as a result of Uralic contact, since such contact certainly occurred; front rounded vowels pattern areally (see jlawler's WALS link above), so a diffusion scenario is not implausible. But I don't actually know of any evidence for it.
(By the way, Attic-Ionic Greek also had /y/, so Germanic languages aren't alone in IE in having this sound; and in Greek it seems to have been a language-internal development, without any contact source.)
As for whether "Germanic phonetics is less similar to the rest of IE", it's no more dissimilar than Irish with its velarized and palatalized consonants, or Indic with its voiced and voiceless aspirates. Lots of IE languages/branches have phonological peculiarities that set them apart from the rest of the family.