Names are usually not enough when looking for Swedes in Sweden. Names that seem fairly rare here usually aren't when you are searching there. It is also best to include posts on the Sweden forum when asking about the origins of a Swedish ancestor. Type Sweden into the "Jump to Forum" space at the top right of this page.
Here is someone with that name who was BORN in Gräsmark parish in Värmland county, Sweden. He didn't leave from there, however. He left from Gudmundrå parish in Västernorrland county, Sweden.
Does his birthdate fit?
Emibas was made from registrations in the Swedish parish to go to a foreign country. It is about 75% complete.
Nilsson Nord, Fredrik Vilhelm Arbetare = worker. (unmarried man)
b. 7/4/1865 in Gräsmark, Värmlands län (Värmland)
Emigrated 4/12/1892 from Sandviken, Gudmundrå, Västernorrlands län (Ångermanland) to Nordamerika
Source: Household Examination Roll, p. 357
Emibas migration file ID: Gudmundrå Y 1892 009
I don't see him (leaving from Gudmundrå parish) on the Emihamn database, made from registrations with Swedish port police when leaving Sweden to go to a foreign country. (Not all Swedes left from Sweden and many in counties such as Värmland and Västernorrland left through a port in Norway. Other countries with popular ports for Swedes include Denmark and Germany.)
On the other hand, perhaps he went to visit his family in Värmland (assuming they stayed there) and left from there. If so, maybe this is your Fredrik Wilhelm Nord. His age fits fairly well. The date of registration is earlier than the date of registering to leave his parish. It could be (I'm speculating.) that he went to visit family and didn't register to leave his parish. Then he ended up registered in Kristinehamn parish for a while and then decided to leave and someone sent word to Gudmundrå parish that he was going to leave the country and maybe he was taken off those books at that time. (Or...this is a different person or... the dates were misread by the transcribers of Emibas or Emihamn or both or... there was an error of some sort.)
First name: WILHELM Last name: NORD Age: 26Gender: M Parish: KRISTINEHAMNCounty: S (Värmland) Port: GÖTEBORG Date: 1892 03 11 (March 11) Destination: NEW YORK Fellows: NEJ Source: 47:218:356
Kristinehamn is not especially close to Gräsmark parish but I do see that Gräsmark parish is close to Norway (Norge). Look at this map.