You can get padlocks which are designed for use without a key - simply a combination of numbers which, when aligned on the barrel part, enable you to unlock by clicking a little button on the bottom of the padlock. I'd suggest that you might look at these, and maybe also consider a padlock and chain on the bike itself.
One problem which arises when thieves can do their "thing" out of sight, is that they have the time to work at it without anyone noticing. The best thing you can do - and this was some good advice from the police and loss adjusters after theft of my property - is that you use several devices/locks which would make it take far longer for them.
As far as keys are concerned, there are several makes of "key box" available nowadays. These are fixed to the wall of a property and (like some padlocks) can be accessed by aligning a number-code. You sometimes see these boxes at properties which are occupied by elderly people who have carers visits - the carer will have been given the key-code and so there's no need to have copies of keys made for their use. Any shop/store which sells disability aids would have them, and I guess that you could find them on the internet as well.
Also (and this is nothing really to do with the original query) - it's a good idea - when you move house - to change all the external locks to your "new" property, as you never know who might have had access in the past.