What we "think" about it is of little consequence. The laws around copyright vary over the world. I think you are being a bit blasé about it. You need some explicit statement of any license you grant. If the publisher makes assumptions and does things you don't approve of with your work you may have little recourse other than a lawsuit that will probably cost you money. As Anonymous Physicist suggests, you shouldn't deal with such people as they are probably not reputable.
If they aren't willing to be explicit prior to publication and ask you to actually sign a clear agreement, then it is a giant red flag.
The risk is yours and yours alone. You may be fine, but no one here can provide any assurance of that. Talk to an IP lawyer to get knowledge of the local laws that will apply.
My worry is, if you give them an implied but not stated license, whether they can pass that license on to others. And, again, if they assume that, then it is a lawsuit that would be necessary to stop it. What "I think" is that you are stepping into a minefield. Don't do so blindfolded.
If you are associated with a university, they may have IP lawyers with whom you can consult.