The surviving records of Old English are relatively prudish. There simply isn't much profanity recorded. There's no question, of course, that people cursed, but we only have records of elite writing. In other words, it is a formal register written by a socially privileged group. That doesn't give us much idea of what colloquial language sounded like.
True, it's not hard to find equivalents for many words that would be considered vulgar today. The direct ancestor of "to shit," for example, is scitan (pron. SHE-tahn). But we don't really know what sort of register the word had. For all we know, it could have had about the same impact as "to defecate." (On the other hand, there is the word skítkarl ("shit-man") in Old Icelandic, which is a general term of abuse.)
To take another example, "fuck" is one of those words that, to judge by its form, may have been in the language from time immemorial. There are, for instance, cognate words in other Germanic languages. But (with the possible exception of a surname "John le Fucker", which may not mean what you think) it doesn't appear in writing until the 15th century. Was it there but unrecorded because it was so taboo, or did this word develop as a euphemism later, perhaps from Middle English "fike" (to fidget)? There are certainly Old English words for having sexual relations, but they tend to sound euphemistic. For example hæman means roughly "to cohabitate" (it's related to ham, "home"). And there's always swifan, "to swive". But again, how much impact would it have had?
Apart from purely lexical matters, there is also the pragmatics of swearing. We can't take it for granted that the set of things we find objectionable would have had the same resonance in an earlier age. Certainly the opposite is demonstrably true. For example, expressions that have their origin in religious figures now often seem quaint (zounds, Mary, by Sainte Loy, etc.). Although we still have "Jesus Christ!" and "God damn it!", the strongest vulgarities today are largely non-religious. The word "profanity"--and "swearing" too, suggests the intimate historical connection between disrespect to the sacred and objectionable speech.
One interesting difference between modern and historical swearing, which may be related to the shift away from religiously-based swearing is the use of the modern curse words as interjections. "Zounds" is an interjection for Shakespeare, but "damn", "fuck", "shit", etc. are not. "Damn" doesn't appear as an interjection before the 17th century. "Fuck" and "shit" aren't so used until the 20th. So if we were to literally translate an expression like "Oh, shit!" into Old English (eala, scite!), we would still be wildly off the mark.
The question then becomes how do you convey to a modern audience that the characters are being vulgar, when a historically plausible form of swearing would not convey the same impact.