You gotta remember the timing though.
Saul went on the run sometime around "Ozymandias".
During that time frame:
Walt was wanted by the police.
Skyler was already with the police.
Jesse was missing.
Huell was missing.
Hank was missing.
Gomez was missing.
Realistically there would be no reason for him to stick around and see if/when he's arrested or killed.
Fred.
In the Breaking Bad series, it would have made sense because of what you mentioned, except for Skylar because she wouldn't be wanting to be implicated. Walt's phone call that episode made it appear he forced her to comply.
But the Nippy episode got me thinking, because he made a decision NOT to run when his cover was blown and able to handle it his own way. Which is something that the OLD SAUL would've done. Add to the fact he was Lalo's attorney, so it wasn't a secret about whom he associates himself with. The only people he MAY have a fear were the Nazi's, but at that stage, he dealt with so many criminals that I've doubt him hiding would be the first immediate option.
By shredding the financial trail connection with Walt, and the police/feds not knowing where the actual money was and Walt disappearing, there was nothing that is SOLID enough pin Saul and at worse, he would just lose his license which was a given anyway.