For quite a while, Hepatitis C was thought to live / be viable (there is some debate as to whether a virus is actually "alive") for up to 4 days. This used to be was was stated on the CDC website. I'm not sure where your doctor would have come up with the 5 minute survival time - that would be the survival time for HIV, not Hepatitis C.
In 2013 some researchers at Yale Medical School did a study on how long Hepatitis C can live outside the body and they found that under the conditions they set up, it could live up to six weeks outside the body. They did say that a large amount of the virus did die rapidly in the first 10 days, but then a small amount that was left slowly died off after that. I do remember them saying that it died off even faster in hot conditions - the 6 week figure was at 70 degrees F but when the virus was exposed to warmer temperatures, it increased the die-off rate. Humidity, pH level, the type of surface it was on and exposure to sunlight also affected the survival time.
I'm not sure why there is the big discrepancy that found that it only lasted 4 days in the original study and 6 weeks in the more recent Yale study. And I can't find any explanation why the CDC (and other sites) are now saying it can live for 3 weeks. I find it hard to believe they would just average out the difference between the two studies and say three weeks. I suppose you could contact the CDC and ask them how they came up with the 3 week time period.
Because you have been exposed to your wife's blood, it does not necessarily mean you have been infected. You need to get the blood into your bloodstream, which means infected blood deep into your body in order to become infected (as in a fresh deep cut, injecting IV drugs, receiving an infected blood transfusion, etc.). And hetrosexual sex is not considered a high risk for Hep C infection by the CDC. An encouraging statistic is that medical personnel who are working on a patient who is positive for hepatitis c and accidentally stick themselves with a bloody needle only get infected at a rate of around 2-3%. Hospitals maintain accurate records of this and anyone who suffers a needle stick must report it to the hospital staff for liability reasons, so the numbers are dependable.
However, you should use universal precautions when coming in contact with any blood, whether it is wet or dry. Always assume that it is infectious material. If you are going to clean it, wear gloves and use a 10:1 water/bleach solution (or any commercial disinfectant that specifically says it deactivates hepatitis c).
And let's not forget that there is now a cure for hepatitis c - expensive at the moment, but with competition between manufacturers, that will change soon.
I've been with my wife for over 35 years and she has not been infected by me. I can't say she's mopped up my blood or any of that during that time, but I've had my share of cuts, nosebleeds, etc. There obviously needs a blood to blood avenue in order to become infected. If you had a gaping wound when you came in contact with your wife's blood, there could be a possibility that you'd become infected.
In terms of the CDC, I respect that they have the resources, expertise, and technology to put forth the utmost testing to determine their findings. They are, in fact, infectious disease specialists. HCV is more resilient than HIV, which has a fairly short lifespan outside of the body. Having said that, and as your doctor mentioned, the CDC likely had a very controlled environment by which they performed their testing. Whether that translates into real-life circumstances, it's anyone's guess.
Your doctor is at the opposite end of the the CDC spectrum, and without scientific data to prove his thinking, it's merely opinion.
Good luck with your test results.