First, it's "shwa". It's a Hebrew word, not a German one, so there's no reason for SCH.
Second, it's both a phone [ə] in IPA, and a phoneme /ə/ in English.
As a phone, it's got the sound of the final vowel in German Danke, of the first vowel in French Le Mans, or the first vowel in English the man. There is no shwa in Spanish or Italian.
Third, as a phoneme in English, /ə/ doesn't contrast with any other central vowel, so it has a lot of allophones: /ə/ [ɨ] [ə] [ʌ] (in increasing order of stress and decreasing order of speed), plus syllabic resonants [ṃ] [ṇ] [ḷ] [ṛ], before those consonants.
The best way I can suggest to practice the sound [ə] is to open your mouth to say an [e] (whatever that you think that is in your language), and then — while saying it, and without changing how your mouth or lips are positioned — move your tongue backwards toward the center of your mouth.
What you wind up saying is likely to be something close to a shwa.
I would suggest: perfunctory
According to dictionary.reference.com:
per·func·to·ry adjective
performed merely as a routine duty; hasty and superficial: perfunctory courtesy.
lacking interest, care, or enthusiasm; indifferent or apathetic: In his lectures he reveals himself to be merely a perfunctory speaker.
This might not fit as a single word for:
a word for faking kindness/hospitality to sound more tactful and
descent than you really are
but you could use perfunctory as an adjective and describe your situation.
I could see through his perfunctory kindness/hospitality.
After some further research, I would recommend you to take a look at this definition of perfunctory here, especially the several examples under it's usage. I found them quite interesting. For instance, these two:
Hers was no perfunctory task; a mother could not have displayed greater interest in her children- "Deaconesses in Europe" by Jane
M. Bancroft
They were not perfunctory, but genuinely genuine- "Priestley in America" by Edgar F. Smith
Best Answer
At a guess (and without a recording it can be no more than that), you are doing one of two things:
If you are merely "overarticulating" the /k/, like an anxious student in a voice production class, you are probably producing a little puff of air when you release the consonant. This sounds like the "BrE" recording on this page, and in IPA it is notated thus: /kʰ/. This is called aspiration; in English it is usually heard only when /k/ starts a syllable and is followed by a vowel, not at the end of a word or before another consonant.
(An unanspirated /k/ before a vowel is often heard among Indian speakers of English; in many subcontinental languages both aspirated and unaspirated stops may appear in this position, and the difference is meaningful.)
If you are really pushing the /k/ it is possible that there is a stretch of time after the release when the tongue is still very close to the palate and air 'hisses' between them. If this is the case you are producing a sound which is not a part of the English phonemic repertory, a voiceless palatal fricative. This is notated /ç/ and is heard in, for instance, German ich, which you may listen to on this page. (Ignore the pronunciation there by Nilreb.)