I think the difference between the two types of examples that you've exhibited is the relative placement in time of the action in the "if" clause, and the action in the other clause.

• If it rains in the evening, we won't go for a walk - here, the event of raining occurs BEFORE the decision about whether to go for a walk.
• My teeth will rot if I eat too much sugar - presumably, I'll be eating the sugar BEFORE my teeth rot.
• If it will significantly increase complexity, don't implement this feature - here, the increasing of complexity occurs AFTER the implementation of the feature.
• I will give you money if it will make you happier - here, you becoming happier occurs AFTER I give you the money.

In all the cases where the "if" part happens first chronologically, we use the present tense. In the cases where the "if" part happens second, we use the future tense. However, because sentences of the first type are far more common than sentences in the second type, a good rule for learners to adopt is "don't use the future tense with IF".

Have you looked at the tense and mode cho­sen for these vers­es in oth­er trans­la­tions that use lan­guages with a more clear­ly de­lin­eat­ed tense and mode in­flec­tion­al sys­tem than English has?

Here are two.

Latin

The Latin Vul­gate has for the first verse’s “The LORD is my shep­herd, I shall not want”:

Do­mi­nus re­git me, et ni­hil mi­hi de­er­it.

where de­er­it is the 3rd sin­gu­lar fu­ture ac­tive in­dica­tive of de­sum, mean­ing to be want­ing or lack­ing (to some­one), and then for the fourth verse’s “I will fear no evil”:

non ti­me­bo ma­la

where ti­me­bo is the first-per­son sin­gu­lar fu­ture ac­tive in­dica­tive in­flec­tion of ti­me­re, mean­ing to fear.

Spanish

The Span­ish Rei­na-Va­le­ra An­ti­gua with its KJV-equiv­a­lent old-timey lan­guage has for the first verse:

JE­HO­VA es mi pas­tor; na­da me fal­ta­rá.

where again fal­ta­rá is the third-per­son sin­gu­lar fu­ture in­dica­tive in­flec­tion of fal­tar, mean­ing to be lack­ing (to some­one), and for the fourth verse:

No te­me­ré mal al­gu­no

where again te­me­ré is the first-per­son sin­gu­lar fu­ture in­dica­tive in­flec­tion of te­mer, mean­ing to fear.

Conclusion

So both the Latin and the Span­ish em­ploy the same sim­ple fu­ture in­dica­tives, with­out any signs of the sort of de­on­tic/epis­temic shad­ing that can in the­o­ry oc­cur with the English modals will and shall.

Be­cause those oth­er two trans­la­tions make no dis­tinc­tion there, I would ad­vise against read­ing too much in­to the KJV trans­la­tors’ par­tic­u­lar choic­es of will/shall in these two par­tic­u­lar vers­es.