Given an undirected weighted graph, we seek a pair of node-disjoint path between $2$ nodes $s$ and $t$: if the objective is to minimize the total path cost, the Suurballe algorithm can be applied; now our objective is to minimize $\max\{C(P_1),C(P_2)\}$, where $C(P_i)$ denotes the cost of path $P_i$, this problem is NP-hard (it is polynomially approximatable in DAG), is there any approximation algorithm for general graphs?

If each edge is also associated a delay, how about the above problems under the aditional constraint that the delay of each path is upper-bounded by a parameter $T$, in this case, is the min-sum version NP-hard? and how about approximation algorithm solving the problems?