Word-final position is special. Full vowel reduction to schwa doesn't occur in general for word-final unstressed vowels, but there are special neutralizations that apply in this context.
The most common word-final unstressed vowels are:
"commA". This is typically transcribed as the phoneme /ə/, but in many accents it is realized phonetically as a more open vowel than word-medial /ə/. It may be something like [ɐ], or similar to the quality of /ʌ/.
"lettER". This is merged with "commA" as /ə/ in a Southern British English accent. In American English, it is a rhotic vowel or a syllabic r, transcribed as /əɹ/, /ɚ/ or /ɹ̩/.
"grottO". In standard British and American English accents, this is just the "goat" vowel (usually transcribed /əʊ/ in British English, and /oʊ/ or /o/ in American English) in an unstressed syllable. In some non-standard dialects, it may be merged with "commA" or "lettER", at least in some words—as a result, the word "potato" has a variant form "tater" that comes from a dialectal pronunciation.
"happY". In a standard American English accent, this is identified with the vowel in the word "fleece", and transcribed as /i/. In British English, there is a bit more variability. Old-fashioned "RP" English used the quality [ɪ] for this vowel, and so at a certain point (Jack Windsor Lewis suggests the first clear evidence is sometime around the 19th century) it became common for British phonologists to identify it with the vowel phoneme /ɪ/.
However, pronunciations with a quality closer to [i] do exist in British English as well as in American English, so recent dictionaries of British English may transcribe it as /i/, using the same vowel symbol as the "fleece" vowel but omitting the length marker. The use of three symbols in transcription should not be understood to mean that there is a three-way phonemic contrast in any form of English between /iː/, /i/ and /ɪ/. It can be analyzed as a neutralization of the contrast between /iː/ and /ɪ/.
In some non-standard accents, it may be merged with "commA" as /ə/, at least in some words. Notably, the American state Missouri has a variant pronuciation ending in /ə/ ("Missoura").
A somewhat less commonly encountered unstressed word-final vowel can perhaps be found in the last syllable of the word "continue". It is possible to analyze this as a "weak" variant of the vowel /uː/, parallel to how the "happy" vowel can be analyzed as a "weak" variant of /iː/. Windsor Lewis says:
What has become a problem for pronunciation lexicographers is that, having given recognition to the weak /i/ of happy etc, they could hardly refuse to recognise the parallel weak /u/ of thankyou for which / `θæŋkju:/ if fully strong must surely sound unnaturally deliberate delivery or a bit of a regionalism. But so far they've done so very grudgingly:both the Longman Pronunciation Dictionary and the (Jones, Roach et al.) English Pronouncing Dictionary give /-u/ for the name of the letter w only in second position. Yet ˈdouble u and ˈw make a quite feasible minimal pair of sorts. For the noun thank(-)you LPD gives only /-u:/ while EPD gives only /-u/. They both agree on recognising (only as a subvariant) /-u/ as a possibility in continue. Only LPD shows /-u/ as possible for value.
The OED doesn't seem to use the symbol /u/ in its transcriptions.
As far as I know, other unstressed vowel phonemes are fairly rare in word-position, but they can occur (except for the "checked" vowel phonemes /ɛ/, /ɒ/, /æ/) and are not reduced. It's unclear to me to what extent a word-final syllable ending in one of the the following vowels should be analyzed as having secondary (or tertiary) stress.
/eɪ/ in essay (which the OED says may have final primary stress in the past), and also for many speakers in Monday etc.--but some speakers have the "happy" vowel in -day.
/ɔɪ/ in alloy, which the OED says used to have final primary stress
/aɪ/ in various words, including Latin plural forms.
A non-final unstressed vowel that comes before a consonant typically can be reduced to /ə/ in at least some accents
As an American English speaker with the "weak vowel merger" (at least, I'm mostly merged in my perception of these sounds), neither /əˈkwɪp mənt/ nor /əˈkɑn ə mi/ seems impossible to me. I would say that the initial vowel in these words can be fully reduced.
Before a vowel, neither "happY" nor the /u/ sound (which I don't know a good example word for) is reduced to shwa--or at least, it's not standard for careful speech. A word like "valuable" may in fact be reduced to something that sounds like "valyable", but the rules for "compressions" like this are rather complicated so I don't know if I can cover them in this post.