Is there a way to query the workstation name for this user?

You can get that from the AppInfo connection property.
[Hint parse that for Host= part of the string that returns]

This may or may not help you though. If you database server is running as a service, and it is logged in as the local 'SYSTEM' account, it may not sufficient network and remote system rights to write to a remote file system.

I guess I have never tried that with BLOBs but you might try:

In case the export needs not be part of a stored procedure or the like but can be done with a singel statement or a sequence of statements, the ISQL OUTPUT command allows a client-side export.

I guess for binary data you need to choose the according format options, possibly something like

 -- a query that should return exactly one single binary value
select MyPfdFile from MyTable where MyDocId = xyz;
output to 'MyLocalPath' format ascii escapes off quote '' hexadecimal asis;

As stated, I'm not sure whether this exports the binary data exactly as it is stored, if not, you might try to specify a particular (binary) encoding within the OUTPUT statement...

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UPDATE: This does not seem to work in my tests with binary data.

I simply don't find a way to prevent the output from containing substitution characters, and there is no "binary" encoding (at least for v12.0.1.4403, I have no v10 setup available).

I have tested with the SQL Anywhere demo database and the products table which has a photo column with JPG images, such as:

select Photo from products where ID = 300;
output to 'C:\\Data\\TestOutputHexAsis.jpg' format ascii escapes off quote '' hexadecimal asis;

and the exported file is not identical to the output via xp_write_file():

begin
   declare binPhoto long binary;
   set binPhoto = (select Photo from products where ID = 300);
   call xp_write_file('C:\\Data\\TestWrite.jpg', binPhoto);
end;

because it replaces values which are not allowed in the (default) encoding with substitution chars such as 0x3F.

(The same procedure should however work with character data.)