SotDL supports a dark fantasy / horror setting. As such, it is inherently unfair compared to other genres. For example it punishes PCs for meeting certain monsters, an event which is completely out of their hands. If you are concerned with introducing fairness there might be other things to look out for besides these stats. They are a good start, though.
Both stats are completely negative. Corruption is a punishment for certain actions, most importantly murder and using dark magic. Removing it would mean that PCs are free to do those things. Murder may have "normal" in-game repercussions (the guards chase you), but dark magic would need something else to balance it. Those spells are much more potent on purpose (another unfairness as NPCs can use them with reckless abandon), so some kind of price should be put in place or they have to be completely removed. For example instead on gaining corruption the caster has to make a Will challenge roll, or lose 2 health permanently.
There are also individual cases. There might be others, but I know of two off the top of my head. The blackguard master path (DLComp 19), which gains corruption with every level. This would not necessarily be properly offset by the above mentioned penalty. You might want to remove the path. The other is the barghest (Core 218), which is more dangerous against characters with corruption. You could simply opt not to use it (I suspect it was included as a punishment for corruption).
This is again a case of having to hunt down all mentions of it in the rulebook and removing or rebalancing them. Saying that horrifying monsters simply do not cause insanity would not be much of a problem, as that rule is mainly there to reinforce the horror genre. But there are paths that use insanity as "currency", risking to gain it in exchange of the use of their abilities, eg. oracles, berserkers and zealots. I suggest you work on rebalancing these only if a player chooses them. (Although zealots are about juggling with insanity, so it might be better to just remove them.)
Another concern might be that removing insanity devalues the Will stat. As there are other uses besides resisting insanity and madness, it is up to you to decide if this is a problem for you. Spells will still use Will attack and challenge rolls and PCs also roll Will challenges to persuade NPCs.
All in all, these are pretty basic / central rules in SotDL. Thus removing them will be much work if you want to rebalance and not just cut out a lot of options. References to corruption and insanity pop up all over the rules, so you have to be prepared to deal with them. Most likely these will come up when you plan an adventure or when a player chooses a path, so you will have time to think about them at least.