documentclass[11pt]{book}
usepackage[backend=biber,style=authoryear,autolang=other]{biblatex}
usepackage[pdftex,colorlinks=true,linkcolor=blue,citecolor=red,urlcolor=magenta,pdfview={XYZ 0 null null}]{hyperref}
usepackage[utf8]{inputenc}
usepackage[T1]{fontenc}

usepackage{filecontents}
begin{filecontents}{bibwithshort.bib}
@book{lagrange_uvres_1867,
  author = {Lagrange, Joseph-Louis},
  editor =       {Serret, Joseph-Alfred},
  title = {Œuvres},
  publisher = {Gauthier-Villars},
  location =     {Paris},
  date = {1867/1892},
  volumes = {14},
  shorthand =    {OL}
}
@article{fraser_joseph_1987,
  title = {Joseph Louis Lagrange's Algebraic Vision of the Calculus},
  volume = {14},
  journaltitle = {Historia Mathematica},
  year = {1987},
  pages = {38--53},
  author = {Fraser, Craig G.},
}
end{filecontents}
addbibresource{bibwithshort.bib}


begin{document}

textcite{fraser_joseph_1987} mentions that in textcite[vol. VII, p. …]{lagrange_uvres_1867}…

  %% Shorthands
  printbiblist{shorthand}

  %% Bibliography
  printbibliography

end{document}

documentclass[11pt]{book}
usepackage[backend=biber,style=authoryear,autolang=other]{biblatex}
usepackage[pdftex,colorlinks=true,linkcolor=blue,citecolor=red,urlcolor=magenta,pdfview={XYZ 0 null null}]{hyperref}
usepackage[utf8]{inputenc}
usepackage[T1]{fontenc}

usepackage{filecontents}
begin{filecontents}{bibwithshort.bib}
@book{lagrange_uvres_1867,
  author = {Lagrange, Joseph-Louis},
  editor =       {Serret, Joseph-Alfred},
  title = {Œuvres},
  publisher = {Gauthier-Villars},
  location =     {Paris},
  date = {1867/1892},
  volumes = {14},
  shorthand =    {OL}
}
@article{fraser_joseph_1987,
  title = {Joseph Louis Lagrange's Algebraic Vision of the Calculus},
  volume = {14},
  journaltitle = {Historia Mathematica},
  year = {1987},
  pages = {38--53},
  author = {Fraser, Craig G.},
}
end{filecontents}
addbibresource{bibwithshort.bib}


begin{document}

textcite{fraser_joseph_1987} mentions that in textcite[vol. VII, p. …]{lagrange_uvres_1867}…

  %% Shorthands
  printbiblist{shorthand}

  %% Bibliography
  defbibcheck{noshorthand}{%
     iffieldundef{shorthand}{}{skipentry}%
  }
  printbibliography[check=noshorthand]

end{document}