Uk Citizen Marrying Us Fiancé Before Applying for Visa

Good afternoon. I would like to know if I am able, as a U.K. citizen, to marry my US fiancé next time I travel there, in around a months time, without first applying for a visa. I have a visa waiver but we’re unsure how US authorities view this and whether we would be suspected of visa fraud. I will be in the US for a week, essentially on a vacation. Is it frowned upon to marry before making a visa application? We were planning on filing for a fiancé visa before getting married but she is pushing to marry next time I’m in the States, saying we can file paperwork afterwards, while I’m still residing in the United Kingdom.

Any advice is greatly appreciated.

Uk Citizen Marrying Us Fiancé Before Applying for Visa