Can signing a dec statement hurt my chances of getting a federal job?

HRC put you on orders because you CAN accept them. As with all branches in the military you are placed on assignment, you can choose to accept the assignment or separate from the active component of the branch. Your declination statement is a statement that says you’re declining to reenlist. You don’t have to sign it, your 1SG can sign for you stating that you decline to reenlist.
You can still apply to a federal job, you can still join the RC, and you will still have an Honorable discharge at ETS.

This is an old personnel technique to thin the heard. You put people on orders for an overseas short-tour location and wait for them to decline the orders After they decline, you put the next service member in line on the same orders. Sooner or later they will find a service member who will take the assignment even if it means reenlisting. In the meantime, the HR folks have forced several folks to make life decisions they may have been putting off.

When I was passed over for O-6, I knew my next assignment would be a 1-year unaccompanied, overseas. I decided to retire instead.

All that will happen with you signing a Dec Statement is you barring yourself from continued service. Guaranteeing you will ETS. Once the Dec Statement has been processed, your orders will be rescinded. And, no...your signing a Dec Statement will not hurt your chances of getting a Federal job.