If the headstock clamp will accommodate a B string you should be ok with an E. If you try it make sure to use heat shrink that reduces 3x rather than 2x or one size might not go tight on all the string gauges. Probably have to go to a real electronics store to find that.
3x and 4x will result in a thicker, rigid plastic around the string relative to 2x. Most 3x I've dealt with are also lined with glue (even when they're not advertised as such), which will also add thickness and rigidity making it harder to clamp down properly, and also make it absolutely miserable to remove the heat shrink.
On a 5-string set a B string will usually be roughly 3 times the diameter of the G. You could reasonably wrap all of them with 2:1 tubing with the follow inner diameters: 3/64", 1/12", 9/64", which corresponds roughly to .047", .083", and .140". A quick skim of Amazon called up a few sampler packs that have those sizes and many others, and can set you up with more tubing than you could ever use for about $5. There will be similar offers elsewhere.
On the other hand, instead of having heat shrink sheath the whole end of the string, maybe a small collar between the clamp and the nut might be enough to prevent any unraveling from extending to the speaking part of the string? In that case, glue-lined heat shrink could be preferable.
Since I'm already taking this idea too seriously, I'll conclude by saying that the heat necessary to apply the heatshrink would probably affect the synthetic wrap or coating on strings that have them. It might be better to leave well enough alone.