If Reuven owes Shimon $10, and shemittah passed, and Reuven remembered he never paid Shimon, yet he still wants to, should he? Is it honorable?
הַמַּחֲזִיר חוֹב בַּשְּׁבִיעִית, רוּחַ חֲכָמִים נוֹחָה מִמֶּנּוּ.
One who repays his debts after the seventh year, the sages are pleased with him.
It's perfectly OK, as Joel K already answered, and actually the lender may even peer pressure him to do so.
However, the money needs to be given as a gift, and not as repayment of the loan, otherwise, the lender may not accept the money.
See the Kitzur Shulchan Aruch in 180:14 who spells out the details.
לֹוֶה שֶׁבָּא לִפְרֹעַ לַמַּלְוֶה חוֹב שֶׁעָבַר עָלָיו שְׁמִטָּה, יֹאמַר לוֹ הַמַּלְוֶה, מְשַׁמֵּט אֲנִי אֶת הַחוֹב וּכְבָר נִפְטַרְתָּ מִמֶּנִי.
אִם אָמַר לוֹ הַלֹּוֶה, אַף עַל פִּי כֵן רוֹצֶה אֲנִי שֶׁתְּקַבֵּל מִמֶּנִּי, מֻתָּר לַמַּלְוֶה לְקַבְּלוֹ מִמֶּנוּ.
וְאַל יֹאמַר הַלּוֶֹה, בְּחוֹבִי אֲנִי נוֹתֵן לְךָ, אֶלָּא יֹאמַר לוֹ, שֶׁלִּי הֵם וּבְמַתָּנָה אֲנִי נוֹתְנָם לָךְ.
וְיָכוֹל הַמַּלְוֶה לַעֲשוֹת הִשְׁתַּדְּלוּת וְהִתְפָּעֲלוּת, שֶׁיֹּאמַר הַלֹּוֶה שֶׁהוּא נוֹתְנָם לוֹ בְּמַתָּנָה. וְאִם אֵינוֹ יָכוֹל לִפְעֹל זֹאת, אַל יִקָּחֵם.
If a borrower comes to pay his debt to the lender after the Shemitah had passed, the lender should say to him: "I have canceled your debt, and you are released from my claims."
If the borrower says: "Even so, I want you to accept the money," the lender is permitted to accept it.
However, the borrower should not say, "I am paying this on the account of my debt;" rather, he should say to him: "The money is mine, and I am giving it to you as a gift."
The lender is [even] permitted to make an effort to persuade the borrower to say "I am giving you the money as a gift." However, if he is unable to [persuade him] he may not accept the money from him.