This question is purely theoretical (i.e. I don't foresee actually trying to use the word), but using arguments based on etymology, as well as euphony and (least importantly) comprehensibility, what is the most etymologically faithful English equivalent for the German Schadenfreude?
Other Germanic languages use etymologically translated calques: skadefryd (Danish & Norwegian), schadevreugde (Dutch). English has a cognate word for German Schaden, Dutch schade, Danish & Norwegian skade, Swedish skada (all of which mean damage/injury) in the form of scathe (which also means damage/injury) – all descended from Proto-Germanic *skaþô (damage/injury) – so it is reasonable to propose that the first part of the theoretical English word should be scath-, scathe- or skaith-.
The difficulty lies with the second part – English does have a word frith (peace/sanctuary) that is a distant cousin of German Freude, Dutch vreugde, Danish & Norwegian fryd (all of which mean joy); but it is a closer relation to German Frieden, Dutch vrede, Danish & Norwegian fred (all of which mean peace), these words and frith all being descended from Proto-Germanic *friþuz (peace). One could opt for –frith : scathefrith is viable.
Or one could take the Swedish option (skadeglädje) and replace the last part with a different word for joy (glädje = gladness) : scathgladness or skaithgladness are options.
The question(s) are which of these three options (scathefrith, scathgladness or skaithgladness) is the best, and is there a better option? Can someone pull a (perhaps obscure, perhaps archaic or even Old) English word out the bag that is a closer relation to Freude/vreugde/fryd? Or perhaps a word with a slightly different etymology that is better for other reasons?
P.S.
Apologies if such questions are not appropriate on English SE, but it is a technical question looking for a technical answer, however theoretical it may be.
Best Answer
Background
English 'schadenfreude', a noun attested from 1867 in OED, derives directly from German schadenfreude, a noun-noun compound. Schade meant "damage, harm, injury", viz.
Freude meant "joy, pleasure, delight", viz.
An Englished meaning of the schadenfreude compound is given by William Dwight Whitney in the 1877 edition of A compendious German and English dictionary as "pleasure at the misfortune of others, malignant joy", viz.
The English meaning given by Whitney in 1877 for the German compound schadenfreude is the meaning retained by the adopted English compound 'schadenfreude' to this day.
Schaden
This investigator accepts the original poster's suggestion that 'scathe' serves well for the first part of the desired "best etymological calque" compound, especially because OED's sense 2a (not shown as obsolete in an entry not "fully updated" since 1910) for "scathe, n." is
Although 'scathe' in this sense is in my estimation obsolescent today (except as found in the participial adjective 'scathing'), the poster of the question indicated that contemporary obsolescence was not at issue for a desirable answer.
Freude
Kluge, in particular, suggested a number of cognates that might be investigated while attempting to find what the original poster of the question announced in comments they were looking for, the investigation target also implicit in the question:
The cognates suggested by Kluge can be supplemented from Deutsches Wörterbuch von Jacob Grimm und Wilhelm Grimm to include "freuen, MidHG", "vröuwen, OHG", "frouwen", and "ahd. frawida, frewida, frowida, mhd. vreude, vröude, nhd. bei".
An exhaustive search of the OED for "obscure, obsolete or even Old English" words derived from any of the cognates suggested by Kluge and the Grimms failed to bear fruit.
Bearing in mind, however, that the original question stipulated "comprehensibility" as of lesser importance than etymology and euphony, and also bearing in mind that there was no indication in the question that complete agreement with contemporary English usage should be desirable, Kluge's suggestion to "see froh" seemed worthwhile. Also, Whitney gave schadenfroh as the adjectival counterpart of schadenfreude, with the meaning "pleased at the misfortune of others, malignant, mischievous".
Froh is glossed by Kluge as "glad, joyous, happy" in English:
Leaping from freude to its reconstructed (that is, unattested) Proto-Indo-European root, *prew-, meaning "to jump, hop", and from there to a posited Proto-Germanic *frawaz, the English word 'frolic' is suggested as a descendant, via Dutch, Middle Dutch and Old Dutch.
OED gave the noun 'frolic' as deriving from either the verb or the adjective; the etymology of the adjective 'frolic' associates the Middle Dutch form vrô with the modern German froh.
Of the etymology of the verb 'frolic', OED remarks that the second element, -licken (Flemish) or -lochen is "of obscure origin".
New Compound
The foregoing suggests that the neologistic compound scathe-frolic serves to answer the question of what, "using arguments based on etymology, as well as euphony and (least importantly) comprehensibility", is the "most etymologically faithful English equivalent for the German Schadenfreude?"
'Euphony', of course, may be considered a matter of personal taste or a matter to be settled by consensus; scathe-frolic sounds pleasant enough to my ear, and seems easy to pronounce. If, as I suspect, the original question meant by 'euphony' something more like sound-similarity than "pleasing and easy to pronounce", the phonic similarity of the first syllable of '-frolic' and the entirety of 'freude', while somewhat slantwise (at least in my pronunciations), is self-evident.
'Comprehensibility', the least important of the stipulations, is in my opinion largely determined by familiarity with the compound used with the particular meaning of "pleasure at the misfortunes of others, malignant joy". However, it might be argued that, absent knowledge of the intended meaning, 'scathe-frolic' would lend itself to, among other interpretations, interpretation as a synonym of 'algolagnia', active or passive or both, where 'algolagnia' is defined as
Other possible interpretations, again absent knowledge of the intended meaning of "pleasure at the misfortunes of others, malignant joy", might involve association with, for example, unlucky outcomes for extreme sports. I suggest, though, that once the intended meaning has been associated with the term, it will come to seem natural — at least as if not more natural than that meaning associated with 'schadenfreude'.