The "knock on your credit is very slight and results from 2 factors;
1) the decreased total amount of credit you now have. SO if you have 3 credit cards with a $10,000 limit on each you have $30,000 worth of credit. Just assume you charge $3,000 a month and pay it off immediately. You are using 10% of your credit limit. If you cancel one card and do not replace it that $3,000 a month charges goes against $20,000 so you are now using 15% of your available credit. This lowers your credit rating. This part can be cured easily by obtaining a new credit card with the same or higher limit.
But unfortunately this comes into play
2) the average age of you accounts can decrease if you have had the card for a long time. For example assume you have 3 cards One you have had for 10 years, one for 5 years and one for one year. The average age of your credit cards is over 5 years. If you cancel the card that you have had for 10 years you will lower our average age to about three years. A big drop. but if you cancel the card you have had for one year the average age goes up to about 7 years resulting in no hit because of average age.
Of course the third factor is;
A)Do you plan any major purchases within the next year.
B) your starting score
If no major purchases are planned then the temporary reduction in your score means nothing to you. Buying a home, new car etc are major purchases. Also car insurance if applying to a new company can be affected. If none of these then you should not be concerned about a small temporary hit.
Lastly if you credit score is great, then a small hit will not affect you. A high score is a high score so if you start out at a FICO of 825 and it drops to 810 it means practically nothing. Your score falls into the "A" category. The hit will last about 1 year before you are back up to the 825
This is a condensed version of the basics so you can make a decision