Short Answer: It can be interpreted in both ways.
Long Answer: 「[noun] + を + 如何せん」 is a common pattern which means 「[noun]をどうしよう」 in modern Japanese, or "What can be done with [noun]?" in English. Usually it implies nothing can be done, or どうしようもない. Of course, を here is an object marker.
In old Japanese, nominalizer こと was not used, and verbs could be directly followed by を, が, etc. Today, this grammar is mainly seen in proverbs (e.g., 負けるが勝ち, 足るを知る者は富む, 聞くは一時の恥).
So you can understand 余命とぼしきを如何せん as 余命が乏しいことをどうしよう in modern Japanese.
That said, I think it is still possible to interpret this を as 接続助詞, and read the sentence as 「余命が乏しいのだが、どうしよう」. The given English translation seems to be based on this interpretation. It doesn't change the meaning of the sentence anyway.
One famous verse which contains this pattern is 垓下の歌. Its third line says 「騅不逝兮可奈何」, or 「騅の逝かざるを如何せん」 in 書き下し文. Most (but not all) of the translations available on the net were along the lines of 「馬が進まないことをどうすればいいのだ」, with the implicit nominalization.