It's wiser to use tool that has feature to update the database directly. for this you have to use all metor tools or cadence tools.
You can use any tools for SI. the drawback for using different vendor tools is everytime you do changes in SI, you'll have to manually do changes in layout re-export the updates file & cycle is repeating....
HyperLynx is used for Signal Integrity. PADS is mainly for Layout. However, i am a little confused about your subject "Analog" signal integrity. SI is generally concerned to the digital realm.