Like others said it totally depends on the project, size, etc. But in general you should be able to go to any engineering firm to have technical drawings made. If it is not huge or heavy or unusually complex then you likely do not need engineering for it anyways. From my experience most municipalities will permit simple signs without an engineer stamp even if the permit application says so. Anything with a large liability should always have engineering done regardless of requirements.
If you are having someone else manufacture the sign then they can likely do all the drawings themselves, no need to pay for the work twice just so they have a nice drawing to work from. If you are doing the manufacturing then make your own production drawings/specs and have that ready if you need any engineer to do load calculations for a stamp.
More details would allow a better answer, but in general you can pick any local firm or an online firm that specializes in sign like mentioned above.
As far as titles go they don't mean much depending on who you talk to, I am a mechanical engineer and at one on my former occupations we had civil, aerospace, composite and industrial engineers all with the same job title doing the same work. The only real thing that matters is that someone has a license to sign off on the final draft.
