Wow. It sure seems like your not getting good directions there. At least the attorney should know better.
Of course you can serve her without a process server! People do it all the time without on. One way is certified mail, of course. But regarding rental property, I can't think of any state that doesn't allow a tenant to be served by posting the docs at their door.
And of course you can serve her yourself. Anyone who is not party to a suit can serve someone, a process server is just a paid non-involved party someone can hire to do it. Whomever serves her simply has to abide by the rules of serving someone and document the serving properly. Since any unlawful detainer suit is only between the landlord and the tenant, you are not party to the suit and thus can serve her.
For instance, people use friends all the time to serve others. I've done it, my brother (an attorney) even used me once to serve someone who his own client was suing. As long as you aren't a party to the suit, there is no reason why you can't serve her.
Leaving her a mouse trap and not making her interact with you to get it.... if you don't want a confrontation, then why let that opportunity go to serve her? I just don't understand that. She doesn't even have to know that you've given it to her at the moment she actually takes possession of it (put it inside the trap); all you have to prove is that you gave it to her. If it's in the trap and she takes the trap, you've served her. All you'll probably want to do is to then say, 'By the way, you've been served with the documents in the envelope inside the trap.'
No offense, but I kind of wonder how competent your area mgr and attorney really are. Serving a tenant is just so, so basic... and easy.