Hand washing is a factor that could leave little to no trace of dna. But as you explained, Adam was very busy, which would eliminate showering as a reason. In fact, based on the factors below and Adams activities outlined in your post, there are more reasons to believe there should have been at least some of Adams DNA left behind. Being there wasnt, I conclude Adam had to be wearing gloves, IMO.
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Factors that can affect the amount of DNA available for transfer include:
Hand washing. If a person has not washed their hands recently, there tends to be more DNA present on the surface of the hands as washing will remove many of the shed cells on the surface of the hands.
Personal Habits. Some individuals tend to touch their face, eyes, nose, hair, etc. more often than others thus picking up DNA from those areas to be transferred onto the next thing that is touched. Wickenheiser (2002) described this process as loading the fingers with DNA.
Type of Contact. Goray et al (2010) demonstrated that factors such as
pressure and friction can also relate to how much DNA is transferred onto a touched object. An increase in the amount of pressure applied tends to lead to an increase in the amount of DNA transferred and the application of friction to the contact increases the amount of DNA transferred even further.
Substrate.
Rough surfaces (wood, concrete, grooved surfaces) tend to collect and retain skin cell DNA better than smooth surfaces. This is why the grip and trigger area of a gun, which are generally rougher, are swabbed for DNA while the smooth areas can be processed for latent prints.
Perspiration. As discussed earlier, sweat is known to increase the amount of DNA available for transfer. It is thought that this may occur for two reasons. First, as the sweat passes through a persons pores and makes its way to the skin surface, it may collect cells along the way and wash them to the surface (Wickenheiser, 2002). Second, the previously mentioned study by Quinones and Daniel (2011) showed that sweat also contains epithelial cells and cell-free nucleic acids which represent additional DNA available for transfer to an object.
http://ryanforensicdna.com/touchdna/