Well I would have to question your assumptions ...
Why would cancelling or scrapping Trident rule out a keeping nuclear deterrent?
ICBM's are inflexible and only really good for blowing the crap out of entire cities or most likely whole countries. They are good as a deterrent and that's about all they are good for. Anyone who actually uses one sign's their own death warrant. That's the MAD concept. Even the soviets got that.
The chances that a country would launch a huge attack against any one else is now very small. The most likely cause would be an accident or a rogue element in the military.
More worrying are terrorists and given their tendency for stupidity, it's a wonder that one of those missing soviet brief-case nukes hasn't been used before now. Difficult to trace and who do you attack in retaliation?
Why not replace Trident with a more flexible missle system which has options to launch various precision non-nuclear weapons as well as lower yield nuclear weapons? Something small and stealthy and keeps the enemy guessing would be ideal lauchable from subs and aircraft would be super.
With modern accuracy you don't need megaton weapons to cause serious damage; surgical strikes against infrastructure would be more effective in the short and medium term. The soviets want for big bangs because their accuracy was very low.
However any use of a nuclear option, even in retaliation might well cause such a backlash from around the world politically and economically that it's use might not be worth the consequences.
Conventional weapons can cause enough damage to make an enemy think twice about attacking. And we are not even taking about bio-weapons or nano-tech which would be far more scary.
An EMP weapon detonated at 10 - 20 miles up would force most modern countries back to the 17th century for a while; probably at least a generation. Screw up their banking systems for long enough and they would be on their knees in quick order. Back to barter and exchange of gold / silver coins etc.
All of those older generation of Plutonium based or triggered weapons can be recycled into new lower power options and civilian power sources at lower cost then having to make the stuff from scratch and keeps the stuff locked up away from terrorists.