‘Else’ is not commonly used in English today but the meaning does fit. From Webster’s (1913):

Else, adverb or conjunction

1. Besides; except that mentioned; in addition; as, nowhere else; no one else.

2. Otherwise; in the other, or the contrary, case; if the facts were different.

“For thou desirest not sacrifice; else would I give it.” – Ps. li. 16.

After ‘or’, else is sometimes used expletively, as simply noting an alternative. “Will you give thanks, … or else shall I?” – Shak.