"In a second the cat runs to me."
Translation:בשניה אחת החתול רץ אליי.
Well, yes indeed. I think that for שְׁנִיָּה second, a full spelling with double-Judh, שנייה, is better than the proposed שניה. You write the consonantal Judh single before a Mater lectionis (the ה indicates only the vowel [a]), but there is an additional חִירִיק before it.