You can always go with a gun in one hand and the knife in the other.
I double up all the time. Last night I used a Glock 22 w/light in my left hand and my M26 Taser w/ laser in my right. I told the runner to put his hands behind his back, he complied, I holstered my Glock, snapped the first cuff on, holstered the Taser, and snapped the second cuff.
It's very unorthodox, because the Taser is officially meant only when there's 2 or more officers, but I rarely have another unit available when I effect an arrest. I have 2 hands.
I work in a nasty barrio, and I project an overwhelming threat of force because I don't want to use any force. I get the cuffs on while they are still trying to calculate their fight chances and escape options, and before I lose that initiative.
Whether you are in a defensive or offensive (I'm apprehending someone) situation, IMO the projection of an overwhelming threat of force often makes makes actual use of force unnecessary. So I project as much force as possible when force may be needed.
If you think you may need to use legal force, and you have a gun, then draw. The knife is a deadly weapon, so you are already statutorily at lethal force once you deploy the knife. Sticking someone is charged or not-charged the same as shooting someone. Sell it to the bad guy, make sure he knows you're committed. Hopefully, he disengages and you can move to safety before he potentially re-engages.
As far as knives go, a $230 Emerson won't deploy faster than a $40 KaBar TDI. The TDI is more rugged, simpler, and IMO it's grip angle is optimized for retention. It slashes and stabs exceptionally well. I can use it blind or disoriented. I carry a TDI on my support side, partially concealed, on duty. I don't carry it off duty, I'm going straight to gun if lethal force comes into play off duty.
I've never deployed the TDI against a human. If someone attempts to handle my duty weapon, then I'm sawing their hand off with the TDI. If someone immobilizes me, then I'm perforating them with either the gun or the TDI. I'm also prepared to articulate how a 300lb'er straddling and thumping me puts me in reasonable apprehension of death. I also have a police agency backing me, a policy that requires only "reasonable action" and prepaid lawyer(s) on call 24/7.
If you have a gun and a knife, and are involved in a lethal force encounter, I'd say deploy the gun in most scenarios.
A switchblade is no more dangerous than any other knife, it simply carries a nastier image and greater projection of force due to that image. IMO, no would-be attacker will read "Emerson" on the side of anyone's blade and be $240 worth of impressed.