My recent etymological proposals in the previous post have turned out to not be news after all. Petri Kallio has informed me that essentially identical etymologies for the Finnic words for “aspen” and “horse”, ie. based on a metathesis of Late Proto-Finnic *ahpa and *ëhpo to *haapa and *hëpo, have been previously proposed by O. Nikkilä, of LÄGLOS fame,  in 1991!
I wonder if we can consider this circumstantial evidence for the validity of the etymologies. :)
A difference though is that Nikkilä suggests the latter to be of Germanic origin as well. Indeed, Germanic *ehwaz explains without complications the *h and particularly *ë: after all, the majority of the Proto-Finnic *ë-words are from Germanic or Baltic, rather than Indo-Iranian.
Getting from Germanic *w to Finnic *p presents some challenges, though, since the cluster /hv/ is perfectly possible in common Finnic vocabulary. But perhaps this is not a decisive obstacle.
From the viewpoint of Modern Finnish, /hv/ can represent several sources, e.g.:
- Most frequently, as a substitution for foreign /f/ in loanwords up to the 19th century, usually thru Swedish. Thus, sohva “sofa”, pihvi “steak” (cf. beef), kahvi “coffee” (only accidentally similar to the original cluster in Turkic kahve, Arabic /qahwa/).
(At the present day, /f/ has however finally made it into the phonology of Modern Standard Finnish, after a persistent siege of about two thousand years: toffee “toffee”, riffi “riff”, etc. It thus seems there will be no more cases of incoming /hv/ for the time being.)
- As an irregular substitution  for Germanic *ww, in the common Finnic *rahvas “folk” ← PGmc *θrawwaz “powerful”.
- As a reflex of EPF *šŋ, in ahven “perch” (cf. Samic *vōsŋōn).
Unclear cases include lehvä “bough” and rehva- “boastful”, which appear to be some kind of irregular derivatives or variants of lehti “leaf” and rehti “honest, reliable”, and the entirely unetymologized kahva “handle”, kohva “frozed snow”, and vahva “powerful”. 
It is noticable that there however do not seem to be any cases that would go back to EPF *šw, or even to a Germanic loan original with *-hw-. So perhaps an explanation similar to what I proposed for the Indo-Iranian path still applies: *p would have been substituted here for phonotactic reasons. Some similar parallels in Germanic loanwords in particular are known. I’ll need to read Nikkilä’s original article of course.
As I mentioned in a footnote last time, already by MPF times there was no shortage of obstruent + *v/*w clusters though. We’d have to date this loan as very early then, perhaps prior to the development *d₁ → *t that created the first of these clusters, *tv. And this definitely means a date long before the shift *š → *h in inherited vocabulary. This would imply that *h actually first arose as a loanword phoneme in Finnic! I’ve suspected as much for a while now, actually. A particularly suspicious case are numerous loanwords where Modern Finnic syllable-final *h corresponds to an Indo-European laryngeal — routing these words thru *š seems very inefficient to me. (I’ve written about this in slightly more detail in an ongoing discussion thread over at Language Evolution.)
I might as well mention here another example of an idea being independently rediscovered that I recently ran into. A 2005 article by J. Koivulehto  presents a Germanic loan etymology for the word family including Finnish painaa “to press”, from PGmc *spannija- “to strain”. To explain the sound correspondences here, he ends up assuming a development PGmc *nj → EPF *ń → LPF *jn. I’ve previously noted that this had actually been already proposed by K. Bergsland decades ago. Koivulehto also rediscovers the inclusion of Samic *puońō- “to dip” in this etymon, and that the development of the long vowel in e.g. PU *küńəl(ə) → LPF *küünel “tear” can be considered supporting evidence for the soundlaw *ń → *jn.
It’s impressive how well different researchers can reach similar conclusions from the same data — and a valuable confirmation that our general methodology of etymological and language-historical research here is, at least, internally consistent.
 I.e. the etymological dictionary Lexicon der älteren germanischen Lehnwörter in den ostseefinnischen Sprachen.
 I can think of a motivation though: perhaps this was adopted after the Gothic/Scandinavian shift from *ww to *ggw, but still sufficiently early that *hv was considered a more acceptable substitute than *kv.
 Though I actually have an idea on kahva. This requires some further investigation yet however so I’ll leave this as a footnote for now.
 Koivulehto, Jorma (2005): Ein neuer autochthoner Grundstamm? In: Finnisch-ugrische Mitteilungen vol. 28/29, pp. 249-255.