Skype rhymes with wipe, tripe, hype, and type. One syllable.

There's definitely no vowel sound on the end. It's nowhere in the spelling and I think you would only here that from other Chinese speakers since Chinese has very few consonants that can appear at the ends of words. The phonetic symbol you used to represent the vowel in the middle won't appear on my phone, but that vowel would be said just like 'ai' in Pinyin.