Yes, you can solder U.F.L connectors.
Yes, you can solder U.F.L connectors.
Yes, you can solder the U.FL connectors onto an M.2 WiFi adapter. It may be tricky due to previous modifications, but soldering is a viable solution if needed.
In theory, it's quite small—you'd need exceptional skill in soldering to achieve it.
Think about connecting it directly and securing it with solder—it could damage the connector and cause a short circuit. If it’s not firmly attached, it might not be making proper contact.
Then soldering wont help, it wont be making contact with the center pin in the first place.