What month of birth was provided on the 1900 U.S. Federal Census?
From Emihamn, here are the two hits you mentioned, but are they the same person? Perhaps or perhaps not.
First name: AXEL Last name: VALLIN Age: 25Gender: M Parish: VIBYCounty: E Port: GÖTEBORG Date: 1894 06 08 Destination: CHICAGO ILLS Fellows: NEJ Source: 53:438:535
Source numbers and emigration days are different for these two people.
First name: AXEL Last name: WALLIN Age: 25Gender: M Parish: WIBYCounty: E Port: GÖTEBORG Date: 1894 06 15 Destination: CHICAGO ILLS Fellows: NEJ Source: 53:601:542
Neither one shows up on Emibas, which is only about 75% complete.
You could probably get the estate inventory (bouppteckning) from a regional archive in Sweden.That would name the heirs and if not in Sweden, it would hopefully name a specific location where the person lived. You'd need to know exactly when and where the people in that bouppteckning died to avoid having to pay the archive for research, however.