How would you change the intensity of a normal map?

This is not how normal mapping works.

Normal maps in UE4 is stored in BC5 format. This is block based compression format that stores only two channels. Only R and G(x and y) channels are stored. Channels are compressed separately. Each 4x4 block stores just two endpoints and each texel just lerp between those endpoints. In shader Z component is recalculated using knowledge/assumption that all normals are unit normals.(length is exactly 1). So: z = sqrt(1 - xx + yy).
All that happens automatically in engine when you use normal map texture compression and normal map sampler. After this point you can make any math for your tangent space normal. In this case you want to change it’s intensity. After this engine transform your normal map from tangent space to world space. Engine also normalize the result. This is reason you don’t have to normalize it after scale operation that actually leave the normal unnormalized.

Lighting code does not care or even know do you use normal mapping or not. It’s totally unrelated.