Clarification in response to comments: I am interested in conversion between tenses/aspects, not specifically in features which sound similar to vav/waw and/or resembling coordinating conjunctions.
As has been mentioned in the comments, forms corresponding to Biblical Hebrew wəqāṭaltí and wayyiqṭol exist in related languages. But these reflect a shared ancestor, or perhaps language contact, and not independent developments. So essentially I understand your question to be whether it occurs in other languages that a morpheme is used to "invert" (part of) the meaning of a form—based on the assumption that waC in wayyiqṭol "inverts" part of the temporal profile of yiqṭol, and that wə in wəqāṭaltí "inverts" part of the temporal profile of qāṭal.
But this assumption is flawed. The waw in neither of these forms is "conversive". This was an idea dating back to medieval grammarians, but has since been abandoned. Scholars don't agree how the Biblical Hebrew verbal system works precisely, but the notion of "conversive" forms cannot count on much support any more. There are several reasons for this.
For one, wayyiqṭol is etymologically distinct from yiqṭol. This can be seen in the forms of the III-ה verbs, biconsonantal verbs, and hiphil forms, all of which have a shortened form in the wayyiqṭol (e.g. wayyagged 'and he told' vs. yaggîd 'he will tell', hiphil of NGD). The wayyiqṭol goes back to a different form of the verb than yiqṭol. In many instances these forms have become identical due to sound changes, so that it seems that wayyiqṭol is based on yiqṭol, but from cases like the three mentioned before (III-ה verbs, biconsonantal verbs, and hiphil forms) it is clear that there were originally two distinct conjugations.
As for wəqāṭaltí, it is not clear that its meaning is really different from that of qāṭal. Most uses can be explained if the meaning of qāṭal is aspectual (perfective). The different stress pattern in some forms of wəqāṭaltí is inconsistent.
Another issue is that the meaning of the "converted" imperfect is not really that of the perfect, and neither is the "converted" perfect identical in meaning to the "imperfect". The wayyiqṭol is found in narrative texts to form the main story line where a distinction is made with qāṭal, which is often used for background information or a past perfect meaning. So it is not correct to say that wayyiqṭol has the same meaning as qāṭal.
All this to say that you are right to find these morphemes (when described as “conversive”) highly suspicious: there may not even be any language that uses morphemes to invert tenses.
A good recent study on these issues in Biblical Hebrew is Cook, John A. Time and the Biblical Hebrew Verb: The Expression of Tense, Aspect, and Modality in Biblical Hebrew. Linguistic Studies in Ancient West Semitic 7. Winona Lake, Indiana: Eisenbrauns, 2012. Of course not everyone agrees with Cook, but the book at least gives a very extensive review.