Given the high packet processing efficiency of programmable switches (e.g., P4 switches of Tbps), several works are proposed to offload the decision tree (DT) to P4 switches for in-network classification. Although the DT is suitable for the match-action paradigm in P4 switches, the range match rules used in the DT may not be supported across devices of different P4 standards. Additionally, emerging models including neural networks (NNs) and ensemble models, have shown their superior performance in networking tasks. But their sophisticated operations pose new challenges to the deployment of these models in switches. In this paper, we propose Mousikav2 to address these drawbacks successfully. First, we design a new tree model, i.e., the binary decision tree (BDT). Unlike the DT, our BDT consists of classification rules in the form of bits, which is a good fit for the standard ternary match supported by different hardware/software switches. Second, we introduce a teacher-student knowledge distillation architecture in Mousikav2, which enables the general transfer from other sophisticated models to the BDT. Through this transfer, sophisticated models are indirectly deployed in switches to avoid switch constraints. Finally, a lightweight P4 program is developed to perform classification tasks in switches with the BDT after knowledge distillation. Experiments on three networking tasks and three commodity switches show that Mousikav2 not only improves the classification accuracy by 3.27%, but also reduces the switch stage and memory usage by $2.00\times$ and 28.67%, respectively. Code is available at https://github.com/xgr19/Mousika.