The wedding shower is for one reason: to gift the bride of the things she needs to start her household. If she already has a household, she does not need a shower.
No, money is never ever asked for as a wedding present, and certainly not at the shower.
"Asked" being the operative word. It is rude to ask for anything.
So they have to wait for a honeymoon. It will be all that more special, when you have to save up and anticipate one.
And wedding guests often take a dim view of honeymoon registries. First off, it takes money up front to get one, and people would rather you spend it on the honeymoon. Second, it is trawling for dollars, telling people that money is wanted. Guests do not want to pay for a luxury honeymoon, when they themselves had to scrimp and save to get to come to the wedding.
I know you mean well, but to surprise the bride with a money shower might just embarrass her to death, that someone broke customary and etiquette rules for a party she had to attend. Let alone her Mom and Grandmom, who would sit there and shudder the whole time.
Do specify on the invite that it is a household, or a kitchen, or a lingerie, or a personal shower.
Like I always say, LOL, this is not the bride's birthday, she is not 8 years old, your guests are not all "Grandma" and you can't get away with telling them what to bring for a present.