As someone who's made a very simple language, I would say there are far too many moving parts involved to guarantee anything of the sort. It's probably better to just integrate libsodium.
Interpreters will literally switch on the type of things in order to figure out what to do with the value. They've lost the side channel battle before it even began. Compilers? Who knows what sort of code they will generate? Who knows how many of your precautions they will delete in an effort to "optimize"? Libsodium has its own memory zeroing function because compilers were "optimizing" the usage of the standard ones.
If you're writing anything cryptography related, you probably want to be talking directly to the processor which will be running your code. And only after you've studied the entire manual. Because even CPUs have significant gaps in the properties they guarantee and the conditions they guarantee them in.
Cryptographers might even consider lowering the level even further. They might want to consider building their own cryptoprocessor that works exactly like they want it to work. Especially if you need to guarantee things like "it's impossible to copy keys and secrets". I own three yubikeys for the sole purpose of guaranteeing this.
