Golfed Solution

'Proposed modification to https://codegolf.stackexchange.com/a/233314/61846
'must be put into a worksheet module
'All cells in the usedrange must hold a value; ie - spaces not blanks
Sub g
Set a=UsedRange
m=a.Rows.Count
n=a.Columns.Count
r=1
c=1
Set u=[A1]
Do
Set x=Cells(r,c)
Set u=Union(u,x)
If InStr(1,"><v^",x)Then:s=(x="^")-(x="v"):d=(x="<")-(x=">")
If x=";"Then Exit Do
r=IIf(r+s<1,m,(r+s-1)Mod m+1)
c=IIf(c+d<1,n,(c+d-1)Mod n+1)
Loop
For Each b In a
If Intersect(b,u)Is Nothing Then b.Value=Chr(113*Rnd+14)
Next
End Sub