Based on some empirical study, in survival mode I do not believe it is correct that LMGs slow down the sprint speed. It looks to me that whatever gun you are carrying, your sprint speed is the same. Things I checked:
- Pistol (Five seven), Shotgun (1887)
- No discernible difference with either weapon equipped.
- No discernible difference with C4 clicker equipped.
- Shotgun (1887), SMG (MP5)
- No discernible difference with either weapon equipped.
- No discernible difference with C4 clicker equipped.
- LMG (L86), SMG (MP5)
- No discernible difference with either weapon equipped.
- No discernible difference with C4 clicker equipped.
- LMG (L86), SMG (MP5) with extreme conditioning
- No discernible difference with either weapon equipped.
- No discernible difference with C4 clicker equipped.
I did notice that the ADS strafe speed with the LMGs is slower than the SMGs, consistent with the multiplayer penalty to larger guns. This seems peripheral to your question though, there is no need to ADS when running.
So in short, running with the C4 clicker doesn't seem necessary. Run with your gun out, it's safer. :)