1

Probably more risk to the animal as well in terms of diseases.

Just don't pick it up, most of these wildlife people on TV violate the most basic rules to protecting wildlife.

2

Don't. Nothing to do with disease. Wildlife has a tough enough time with the way the human race treats the environment. They want to survive and it is a struggle for them. Picking them up does not help them. After you have picked them up and petted them, they don't go away thinking "how nice, what a pleasant person, etc.". At best you have disrupted their foraging/put them under stress/blown their cover from predators/etc. Basically, all you will do is make their lives and survival harder. Different animals will react differently, your impact ranging from bad through to death.

On occasions I can appreciate that wildlife documentaries do disrupt wildlife and have a negative impact and there is sometimes/often a justification based on needing people to appreciate how fantastic these creatures are and to appreciate the need for conservation. However, some presenters take this too far and there is no need to pick-up/start petting and film can illustrate the beauty of wildlife without such an invasion into their lives.

Of course you might get bitten, might catch a disease, etc. - but there are far stronger reasons not to do it.