Is "sans" a drop-in replacement for "without"?

Solution 1:

Well, Merriam-Webster considers sans a word (meaning without). Sans-serif is definitely correct; that is simply what sans-serif fonts are called. Shakespeare used it like this:

My love for thee is sound, sans crack or flaw.

I think it's safe to assume that if Merriam-Webster and Shakespeare use it, it's probably a safe word to use; the words that weren't words when Shakespeare used them became words anyways.

As for how much one should use the word, I would suggest limiting its use, despite the fact that it may be legitimate; using it could make you sound silly (awkward wording sounds silly, IMO) or pretentious.

Solution 2:

The Oxford English Dictionary describes it as archaic.

Solution 3:

As others said, sans does mean without. However, in my experience it is used only to modify a noun, not a verb phrase. So your "sans using" example feels very wrong to me, but "sans serif", "sans pickles", etc are fine. (Another answer commented on the oddness of "sans my brother", though "sans Dave" feels more natural.)

So sans is best used with an unmodified noun, might be ok with a modified noun ("my brother") but will sound "off", and is not advised with verbs.