Definitely don't bother with a tutor. If he's not picking up phonics from the work his teacher is doing with him in class he's not ready yet and you'd be throwing your money away.
The approach of teaching 'tricky' sight words separate from phonics is because the English language is very complex and many of the high-frequency words which appear regularly in their books can't be sounded out as they haven't learned the code for it yet (eg the, to, no, go, he, she, was, my etc).
Children 'get' blending at different times, it takes some a lot longer than others. I often find some children pick up the tricky words quickly, as that's how their brain works, and yet they're still struggling with can, had, big, run etc. As a Reception teacher I see no harm in using flash cards for those who struggle with phonics but are picking up sight words. The theory behind teaching phonics is because the human brain only has the capacity to memorise so many hundred words (apparently), so we we need to teach children strategies to work out unfamiliar words which are phonetically decodable. So keep plugging away with blending games, but there's no harm in adding in a sight reading approach too to help him on his way. If he can learn to recognise several vc and cvc words by sight, it will give him a confidence boost if nothing else. I often add them in at this time of year anyway as I want children to start recognising them even if they can blend. It can be frustrating hearing a child read the sentence 'They went on a bus and had fun' (for example) and the only word they read by sight is they! If they can read they, because they have memorised it, they definitely should be able to do the same with 'on', 'and', 'had' etc if they're shown them enough times!
40 words by sight at only half way through Reception sounds incredibly optimistic though, I'd be happy with 50 by the end of the year (on average, obviously some children will be well beyond this and others will know a lot less). To say he 'should' know 40 by sight already, only halfway through the school year, is unrealistic expectations. Talk about putting pressure on children and labeling them as behind an early stage.
Ideas to help the blending process:-
Play I spy by sounding out CVC words, eg I spy with my little eye a b-i-n, or a m-a-t etc.
Give instructions in robot talk whenever you use a CVC word, eg s-i-t down, or g-e-t your c-oa-t. Z-i-p i-t u-p etc.
Animal noise game. Ask what noise a d-o-g makes? What about a d-u-ck? What does a p-I-g sound like? etc (could also do hen, cat, sheep etc) . Or ask him to point to body parts on command. Where is your n-e-ck? (Back, chin, leg, lip, foot, cheek etc)
Children need to be able to orally blend before they can do it with words in a book.