Difficult question that I don't think anyone has a definite answer on but I'd refer you to this article

https://www.science.org/content/blog-post/myth-ethidium-bromide

For the carcinogenicity risk and according to the International Agency for Research on Cancer (IARC) as mentioned in the attached SDS file "No component of this product present at levels greater than or equal to 0.1% is identified as probable, possible or confirmed human carcinogen." For the mutagenicity risk, it mentioned that there is a mutagenic effect in germ cells.

Dear Evelyne, many thanks for sharing this important technical question with the RG community. The question is certainly of broad interest to many other RG members who regularly or frequently work with ethidium bromide. Clearly ethidium bromide is mutagenic, but there is no sound scientific evidence for carcinogenic effects. A spilling accident might have been responsible for cancer cases several years later, but this is nearly impossible to prove. Possibilities of getting in contact with ethidium bromide are inhalation, ingestion, and skin absorption. Thus you should always handle the compound with great care in a fume hood and always wear protective gloves.

I hope this helps. Good luck with your work and please stay safe and healthy!

Looking to the Safety guidelines

https://www.sigmaaldrich.com/IT/en/sds/sigma/e7637

it is reported as H341 (mutagen) and not H350 or H351 (cencerogenic)

However there are several reagents less toxic that could be used to replace it.

eg.

https://proteocool.blogspot.com/2021/05/tips-of-week-4-replacment-of-ethidium.html

Ciao

Manuele