Citing/Referring: How to have a parencite without bracket ( )?

Usually (e.g. in the biblatex standard styles without modifications that say otherwise), cite gives the result that parencite would give you, just without the parentheses.

documentclass[british]{article}
usepackage[T1]{fontenc}
usepackage{babel}
usepackage{csquotes}

usepackage[backend=biber, style=authoryear]{biblatex}

addbibresource{biblatex-examples.bib}

begin{document}
Lorem autocite{sigfridsson}
ipsum parencite{sigfridsson}
dolor cite{sigfridsson}

printbibliography
end{document}

So the first thing I would try is cite.

Without having seen your code I can't tell if that will work as you hoped it would, though. It is hard to say what the most elegant way to achieve the result you want to see is in your setup, but the following should work provided the definition of parencite from the question does the right thing. You can simply copy the definition of parencite, give it a new name and drop the [mkbibparens], which produces the parentheses.

documentclass[british]{article}
usepackage[T1]{fontenc}
usepackage{babel}
usepackage{csquotes}

usepackage[backend=biber, style=authoryear-comp]{biblatex}

DeclareCiteCommand{parencite}[mkbibparens]
  {renewcommand*{postnotedelim}{addcolonspace}%
   usebibmacro{cite:init}%
   usebibmacro{prenote}}
  {usebibmacro{citeindex}%
   printtext[bibhyperref]{usebibmacro{cite}}}
  {multicitedelim}
  {usebibmacro{postnote}}

DeclareCiteCommand{nparencite}
  {renewcommand*{postnotedelim}{addcolonspace}%
   usebibmacro{cite:init}%
   usebibmacro{prenote}}
  {usebibmacro{citeindex}%
   printtext[bibhyperref]{usebibmacro{cite}}}
  {multicitedelim}
  {usebibmacro{postnote}}

addbibresource{biblatex-examples.bib}

begin{document}
Lorem autocite[381]{sigfridsson}
ipsum parencite[382]{sigfridsson}
dolor nparencite[383]{sigfridsson}
sit cite[384]{sigfridsson}

printbibliography
end{document}