First, in Basel
(BS and BL) your dogs are not classed as dangerous dogs due to their size.
It is true that in some cantons dogs over a certain size are classed as potentially
dangerous - note this is not the same as being classified as dangerous - and so have additional requirements to be met, this is not the case in either of the Basels.
This is hard for many newcomers to understand, but in Switzerland there are three levels of dog law. First there is federal law, which applies to all in Switzerland. Then there is cantonal law, there are 26 different sets of dog control laws, what is forbidden in one canton is of no consequence in another. Lastly, there are Gemeinde regulations to be adhered to. So when you read a post please note the canton and Gemeinde, as the rules will vary widely.
To make it even more confusing, many Swiss blatantly ignore the laws. How strictly the law is enforced varies widely as well, from canton to canton and Gemeinde to Gemeinde - and even from person to person.
But as a newcomer I would urge you to follow the law. That so many here refuse to comply with relatively mild regulations is a reason why increasingly draconian measures have been put into place. As always, it's the responsible owners and their dogs who suffer, while the scofflaws bear no consequences.
But be that as it may...
Do you read German? If so, here are summaries of the laws in Basel Stadt and Basel Land, compiled by the foundation Tier Im Recht. The actual text of the cantonal law is linked at the top of each page.
Basel Stadt: http://www.tierimrecht.org/de/tiersc...asel-stadt.php
Basel Land: http://www.tierimrecht.org/de/tiersc...basel-land.php
As you can see, the dogs on the 'dangerous' list in both Basels are:
Rottweiler, Dobermann, American Staffordshire Terrier, Pitbull Terrier, Bullterrier inkl. Miniatur Bullterrier, Staffordshire Bullterrier, Dogo Argentino und Fila Brasileiro - and any dog with one of these breeds in the mix.
So, as long as your dogs do not have any of the restricted breeds in their background, you will not have to worry about 'dangeous dog' restrictions.
In addition to the regulations around keeping breeds deemed dangerous, the regulations - where leash restrictions apply, where dogs are forbidden, quiet times, forest/seasonal regs, etc - that apply to dog owners are listed. Do you need a translation? If so please say so, as well as which canton you are going to live in, and I'll post a translation of the summary for you.
So - what this boils down to is that you will need to comply with the federal regulation, which are the SKN courses.
There are two required courses, the Theory and Practical. The SKN Theory course is required of all first time dog owners - defined as not having had a dog registered in your name in the ANIS database. Of course you are not a new owner - but you also have not had a dog in Switzerland before. In such cases, you need to contact the cantonal Veterinäramt for a ruling as to whether your proof of previous ownership is sufficient to excuse you from the requirement, or not.
(I always recommend that newcomers to Switzerland take the Theory course even when not required, as the various dog laws are discussed. This might be your best opportunity to learn all that you need to know about dog ownership in Switzerland.)
The second required class is the SKN Practical course, required of all dog owners who acquired their dog after 1 Sept 2008. Now your 15 year old dog is excused, but you should take the course with your 5 year old female. You have a year to do the classes.
The SKN classes are very basic, they just skim the surface, any responsible experienced owner will have no trouble whatsoever taking the class. There is no test, attendance is all that is required. The courses are inexpensive, ca. 150-200 each.
As above, some Gemeinden are very strict on enforcement; mine is one such. I am required to give a copy of my SKN certificates to the Gemeinde - and they will chase down any scofflaw owner. But as we have seen over and over again, not every Gemeinde is so strict.
In the federal law, compliance with the SKN courses is left to the honor system - naively perhaps, but it was assumed that Swiss dog owners, of course being honorable, would comply without external mechanisms to enforce the law. Sadly, we have seen that honor seems to be a commodity in increasingly short supply.
And please be aware of another rather Swiss approach to regulations, all regs not just dog law: Generally, the onus is on you to learn the law, not on the regulatory authority to make you aware of the law.
But do be aware that even in Gemeinde where the law is not enforced as a matter of course, if you are brought up on another dog related infraction your SKN status might be checked as part of the investigation. This is where the fines have been levied, as you can see from the Tierschutzstraffälle database.
So - don't worry, assuming that your dogs do not have any of the restricted breeds in their mixes they are allowed in Basel without extraordinary measures. But do make sure you understand cantonal and commune regulations, and follow them. (Even when your neighbors don't.)
In fact, since you mention that your younger dog isn't socialized to urban areas, I would recommend going beyond the SKN Practical course and continue with something like Familienhund classes. Continued courses are a great way to socialize a dog to 'Swiss standards' - not to mention fun for your dog, a great way to meet new people, hopefully some who will become friends, and find your feet quickly in your new country. My dogs and I enjoy Familienhund as a regular activity - it's far more than just a class.
Wishing you and your dogs all the best as you settle in.