The extracted activations can be used as any conv input, i.e. you can treat them as a new “image tensor” with 4 channels and a spatial size of 56x56.
To do this, you would have to change the number of input channels of the first conv layer of your new model to 4. Also, since your spatial size is now smaller, you should change the number of input features for self.fc1 to 256.
This code should work:
class ConvNet(nn.Module):
    def __init__(self):
        super(ConvNet, self).__init__()
        
        self.conv1 = nn.Conv2d(4, 64, kernel_size=11, stride=4, padding=2)
        self.pool1 = nn.MaxPool2d(kernel_size=3, stride=2)
        
        self.conv2 = nn.Conv2d(64, 192, kernel_size=5, padding=2)
        self.pool2 = nn.MaxPool2d(kernel_size=3, stride=2)
        
        
        self.conv3 = nn.Conv2d(192, 384, kernel_size=3, padding=1)
        self.conv4 = nn.Conv2d(384, 256, kernel_size=3, padding=1)
        
        self.conv5 = nn.Conv2d(256, 256, kernel_size=3, padding=1)
        self.pool5 = nn.MaxPool2d(kernel_size=3, stride=2)
        
        self.relu = nn.ReLU()
        
        self.drop_out = nn.Dropout()
        self.fc1 = nn.Linear(256, 4096)
        self.fc2 = nn.Linear(4096, 4096)
        self.fc3 = nn.Linear(4096, 1)
        self.relu = nn.ReLU()
        self.sigmoid = nn.Sigmoid()

    def forward(self, x):
        out = self.pool1(self.relu(self.conv1(x)))
        out = self.pool2(self.relu(self.conv2(out)))
        out = self.relu(self.conv3(out))
        out = self.relu(self.conv4(out))
        out = self.pool5(self.relu(self.conv5(out)))
        out = out.view(out.size(0), -1)
        
        #out = self.drop_out(out)
        out = self.drop_out(out)
        out = self.relu(self.fc1(out))
        out = self.drop_out(out)
        out = self.relu(self.fc2(out))
        out = self.sigmoid(self.fc3(out))

        return out
    
model = ConvNet()
x = torch.randn(6, 4, 56, 56)
out = model(x)