You can use CreateProcess to launch a hidden copy of the cmd.exe format command, and feed it characters to handle the prompting. This is in Pascal, but it's all API calls, so it should translate pretty easily. You'll need to add some error handling too, and make sure you test it extensively.
Win32_Volume::Format was only added in Windows 2003, so it won't work if you need WinXP or Win2K support.
procedure FormatFloppy;
var
sa: TSecurityAttributes;
si: TStartupInfo;
pi: TProcessInformation;
BytesWritten: LongWord;
hInRead, hInWrite: THandle;
begin
// Initialize security information
sa.nLength := SizeOf(sa);
sa.lpSecurityDescriptor := nil;
sa.bInheritHandle := True;
CreatePipe(hInRead, hInWrite, @sa, 0);
// Initialize startup info
ZeroMemory(@si, SizeOf(si));
si.cb := SizeOf(si);
si.dwFlags := STARTF_USESHOWWINDOW or STARTF_USESTDHANDLES;
si.wShowWindow := SW_HIDE;
si.hStdInput := hInRead;
si.hStdOutput := GetStdHandle(STD_OUTPUT_HANDLE);
si.hStdError := GetStdHandle(STD_ERROR_HANDLE);
// Start process
ZeroMemory(@pi, SizeOf(pi));
CreateProcess(nil, 'cmd /c format a: /fs:FAT /F:1.44 /V:', nil, nil, True,
CREATE_NEW_CONSOLE or NORMAL_PRIORITY_CLASS, nil, nil, si, pi);
CloseHandle(pi.hThread);
CloseHandle(hInRead);
// Write '<enter>' to start processing, and 'n<enter>' to respond to question at end
WriteFile(hInWrite, #13#10'N'#13#10, 5, BytesWritten, nil);
CloseHandle(hInWrite);
// Wait for process to exit
WaitForSingleObject(pi.hProcess, INFINITE);
CloseHandle(pi.hProcess);
end;