Storing the silverwing for the a couple of months with no garage

If I have to store my 2005 silverwing for a couple of months and don’t have access to a battery recharger /outlet Outside  — should I just remove the battery and have the recharger - trickler  charge the battery at home ?

Yes, removing battery is a good idea, cover airbox inlet and exhaust, but do not seal with plastic, use rags, etc., a proper bike cover that breathes is always best(tarps   ) , try to position out possible windy areas, etc.
On side stand, parking brake set, piece of wood or metal under side stand, JIC. is best outside.

Why don't you hire a storage unit for a couple of months. I had to put my Silver Wing in a storage unit for 6 or 7 weeks way back, and the only condition stipulated was to ensure the fuel tank was low before storing it.

I wheeled the scooter into the storage unit, hauled it up onto it's main stand, put the steering lock on, and that was all.

When I took it out of storage, I took my Optimate charger with expecting to have the put the battery on charge for a few hours on the ground floor. It wasn't necessary as the Silver Wing started first press of the button, I already checked the tyre pressures and they were fine too.

So it was round to the nearest supermarket to fill up with fresh fuel, and then home the long way.

If I was storing any bike for a few months I would be concerned about surface corrosion, the battery, vermin, and the fuel. We're not big on ethanol here (yet) but I hear bad things about fuel going off, so I would have a full tank (less chance of corrosion on the tank inside) and add a fuel stabilizer. Remove the battery and trickle charge it. I don't think the SW has an airbox that would appeal to critters (Honda VFRs and STs seem like mouse magnets however) but have seen some bad things with chewed wires; not sure whether this is a concern wherever you are. Maybe coat the exposed fork tubes with some grease to stop them rusting. Overfill the tyres (and drop back to normal pressure before riding) to stop any flatspots developing.

A good cover is absolutely essential especially if you get any wind. I bought cheap covers and they tear up in a short time.

I bought this cover for my Goldwing 1800 and used it on my Yamaha V-Star. Now it fits on my Forza! A bit big but not a problem, have been using this one for 5 years and it is wearing like iron. My Silver Wing rests in a covered garage but my Forza doesn't have that luxury. So I highly recommend the below cover, in fact it is on sale right now:

https://www.cyclegear.com/accessories/bilt-deluxe-motorcycle-cover