Another method to convert a copied text to kana is to copy it into Word, select the text and hit 'Shift+Space' (in kanji mode). It will slice up the sentence and allow to convert any part to other kanji readings or kana, as if you'd have typed it in yourself. Pressing Esc twice will convert the whole thing to hiragana. Pressing Esc a third time will cancel the operation; you need to press Enter for the conversion to take effect.
It will only offer one kana reading, so if you selected '今日', it will only show 'きょう' and its alternatives, not 'こんにち'. (But like in Excel, if you typed it in yourself, it will remember your spelling.) It also limits the range of the selection, the length depending on a number of factors, so converting a whole text may take a while, but should still be faster than typing it in manually.