I would probably use NOT regexp_like, which is more clear. But since you mentioned you don't want to use NOT, then I would probably use this (again, more clear imo):
select 'Does NOT contain dash or underscore' as val
from dual
where regexp_instr('ABC123', '[-_]') = 0;
I'm sure you'd have about 20 different regexp versions soon ;-)
If you care about special treatment of empty strings(nulls), use a simple nvl:
nvl(regexp_instr('', '[-_]'),0) = 0;
I mention this because using regexp_like does not allow for this (nvl isn't a relational operator, but in this case we're comparing instr to a number, so we can use nvl on the instr (left hand) part.
But granted this depends on whether you want to say anything about the existence or non-existence of some characters in a null ;-)