By squeezing the electric hot water bottle too tightly (a hot water bottle of very bad quality) the liquid leakes, wetting me and my partner (especially in pajams, but also on the skin). if the liquid was carcinogenic, can in this case cause cancer?

Probably there is no possibility of any health problem from such contact. The fluid probably is water, perhaps with a disinfectant. You should be able to find out by contacting the manufacturer. But I see no cause for worry.

There is little risk of cancer from what you described. You can reduce your risk of cancer by adopting healthy habits: Eat a mostly vegetarian diet, avoid alcohol, tobacco and street drugs, avoid excessive exposure to sun, maintain healthy weight, get HPV vaccine, exercise 30 minutes each day, drink enough water so your urine is mostly colorless. Wish you good health!