Some source I found counts about 43,000 Icelandic "base" words, which gets inflated up to something like 610,000 when you count compound words and words with pre/suffixes, but that's from a survey of written documents since the 1500s, so it probably includes quite a few obsolete words. Theoretically you could go on making compound words forever in Icelandic, since we use compounds for a lot of cases where English would use multiple words and people spontaneously make up compound words for the purposes of a single conversation all the time; about 519,000 of those 610,000 were compounds, and about half of the compounds only appeared once across all those documents. The same source's list of words in spoken Icelandic includes about 50,000 words, but I don't know how the methodology for that number works.
So, yeah, a considerably smaller language than English if you drop the spontaneous compounds.
Probably most problematically for this particular sort of thing, Icelandic has a lot of vowel shifts in the stems of even regular words between forms, so forms of one word may actually look like a completely different word, and two different vowels can be shifted into the same vowel so that you can't tell what the original word is just from seeing a form of it, even if you do have a list of what vowel shifts are possible. Meanwhile vowel shifts can also distinguish between completely different words that are completely different in meaning, and there are about a bazillion different inflection classes of everything that have different endings in different cases, such that the total number of things that might be inflection endings is pretty massive, and of course a lot of the time those same endings just happen to be part of the root word and not actually inflection endings.
So, like, the "Önnu" in my name is the genitive case of the name "Anna". But there is also a word "önn" (semester), and a word "önnur" (another, feminine), and both -u and -ur are common inflection endings, so if you chopped them off, you'd end up with all those being lumped together. And then if you want to be able to group "Önnu" with "Anna" and try to account for some other inflection patterns where n's can get doubled up, you might end up with stuff like "andi" (genie) in there as well (-di is a past tense verb ending), plus the verb "ana" (rush). And lest you try to use the endings to deduce word classes and only lump things together if you deduce them to be in the same class, of course most endings are used in a bunch of different contexts for different classes of words, e.g. -ur can be a nominative ending for some masculine nouns, or a nominative ending for some neuter nouns, or a nominative and genitive ending for some feminine nouns, or a masculine ending for some adjectives, or a third-person singular present tense ending for some verbs.
Ahh, that makes a lot more sense on "bodily". Doesn't seem like it'd be too hard to keep track of what -y words have been manipulated and just change them back, though.