Could you try the following definition:
class cauchy_activation(nn.Module):
    def __init__(self):
        super(cauchy_activation, self).__init__()
        
    def forward(self, x):
        return pdf_cauchy_distribution(x)

model = models.resnet18(pretrained=False)
model.layer4[1].relu = cauchy_activation()
output = model(torch.randn(1, 3, 224, 224))