Chacham: No Problem! It is my priviledge to recite Hallel on Yom ha’Atzmaut.
As for your assertion Sam2, that the Availus corresponds to Yud Beis Chodesh, let me assure you it is more lenient:- If you Sam2 observe the 1st 33 days as the mourning period, and your buddy who keeps the 2nd part invites you to his/her wedding during the last week of Nisson, you definitely are allowed to attend the entire Chasuno including dancing to the music:- The mere fact you won’t be shaving before attending your buddy’s wedding suffices to count this towards your 33 day quota, despite the music. Yet the guy in Yud Beis Chodesh could not attend this nor any other Simcha {unless very close relative}.