Yes, it's possible and a broken blister isn't even necessary. A number of diseases can be transferred from person to person by contact with intact skin or objects skin has touched such as doorknobs and... kettlebells.
One of the most common modes of transmission is the fecal-oral route, which is explained below.
Source
Some infections are spread when microscopic amounts of faeces (poo)
from an infected person with symptoms or an infected person without
symptoms (a carrier) are taken in by another person by mouth. The
faeces may be passed:
directly from soiled hands to the mouth indirectly by way of objects,
surfaces, food or water soiled with faeces. Examples of diseases
spread from faeces:
- Campylobacter infection
- Cryptosporidium infection
- Giardia infection
- hand, foot and mouth disease
- hepatitis A
- meningitis (viral)
- rotavirus infection
- Salmonella infection
- Shigella infection
- thrush
- viral gastroenteritis
- worms
- Yersinia infection.
So instead of worrying about the blisters on your teammates' hands, you should worry about how well they wash their hands after using the toilet.
Other diseases can be spread by direct skin-to-skin contact or indirectly through a common object two people touch. Although there are only a few diseases that can be transmitted by direct skin-to-skin contact of intact skin, people are prone to touching their eyes, nose and mouth, so you have to include diseases that can be spread by contact with mucous membranes as well.
Some infections are spread directly when skin or mucous membrane (the
thin moist lining of many parts of the body such as the nose, mouth,
throat and genitals) comes into contact with the skin or mucous
membrane of another person. Infections are spread indirectly when skin
or mucous membrane comes in contact with contaminated objects or
surfaces.
Examples of diseases spread by skin or mucous membrane contact:
- chickenpox
- cold sores (herpes simplex infection)
- conjunctivitis
- hand, foot and mouth disease
- head lice
- molluscum contagiosum
- ringworm
- scabies
- school sores (impetigo)
- Staphylococcus aureus infection
- warts.
What can you do about this? Wash your hands frequently and develop a habit of never touching your eyes, nose, lips and mouth with your bare hands. This is why many gyms provide disinfectant wipes to wipe down exercise equipment after you've used it, but hand washing is more effective.