I am afraid Windows doesn't support this natively AFAIK, you will have to create a logic yourself, if the whole filename is interpreted as an extension, then there is no filename without extension, you can use this in PowerShell:
if (-not ([System.IO.Path]::GetFileNameWithoutExtension($File))) {&"$Env:ProgramFiles\Notepad++\Notepad++.exe" $file}
If you can put this or some other logic similar to this in registry somehow, then you can double click on the files to open them with Notepad++(or do assoc and ftype for everyone of them...).
The above script is an if statement, it only executes only if the if condition is true, -not is a logical operator that means "not", in here it means "not exist", [System.IO.Path] is a PowerShell class, GetFileNameWithoutExtension() is a .Net method which does exactly what it says; $File is a variable, the whole block in () is a condition, which means "not exist filename without extension", the block in {} is a command block, $Env is for calling Environment variables, $Env:ProgramFiles equals to %ProgramFiles% in cmd, usually it is "C:\Program Files", the string in "" is the path to Notepad++, & is a call sign, used to invoke the executable at the path, the command block opens the file with Notepad++;
To use it, replace the variable $file with the full path of the file, the path must be enclosed in double quotes, or run: $file="path\to\file" first, if you want to use another program, replace path to Notepad++ with full path of the program, also enclosed in double quotation marks...