For a compact orientable PL $4$-manifold $M$ with boundary, let $\hat{M}$ be the singular manifold obtained by capping of $\partial M$. In this article, we explore the class of compact orientable PL 4-manifolds with empty or connected boundary, whose fundamental groups have rank 1, and their corresponding singular manifolds admit weak semi-simple crystallizations. First, we show that if $M$ is a closed orientable PL 4-manifold belonging to this class, then there exist complementary submanifolds $V$ and $V'$ with a shared boundary such that $\mathcal{G}(V')\geq\mathcal{G}(M)\geq\mathcal{G}(V)$, where $\mathcal{G}(M)$, $\mathcal{G}(V)$, and $\mathcal{G}(V')$ denote the regular genera of $M$, $V$, and $V'$, respectively. Next, we provide a handle decomposition for a compact orientable PL $4$-manifold $M$ with connected non-spherical boundary from this class. If the rank of the fundamental group of $\hat{M}$, $m'$, is $1$, then $M$ admits a handle decomposition that takes one of the following forms:<br> 1) one $0$-handle, one $1$-handle, $k$ $2$-handles and one $3$-handle, where $k=2+\beta_2(M)-\beta_1(M)-\beta_1(\hat{M})$, or<br> 2) one $0$-handle, two $1$-handles, $k$ $2$-handles and one $3$-handle, where $k=3+\beta_2(M)-\beta_1(M)-\beta_1(\hat{M})$.<br> Further, if $m'=0$, then $M$ admits a handle decomposition which consists of one $0$-handle, one $1$-handle and $\beta_2(M)$ $2$-handles.<br> We further demonstrate that no manifold from this class with empty or connected spherical boundary can have a fundamental group isomorphic to a finite cyclic group. Finally, we provide a handle decomposition for such manifolds with empty or connected spherical boundary.