I think I should quote the German HGB section you’re asking about, as I don‘t particularly trust the English version of it:

(1) Ist der Käufer mit der Annahme der Ware im Verzug, so kann der Verkäufer die Ware auf Gefahr und Kosten des Käufers in einem öffentlichen Lagerhaus oder sonst in sicherer Weise hinterlegen.
https://www.gesetze-im-internet.de/hgb/__373.html

That’s relatively easy to find when looking for British T&Cs:
"…the Seller may…charge the Buyer with the cost of storage from the date the goods were tendered for delivery, the cost of any additional transport…"
https://everett-art.co.uk/terms/

(2) Er ist ferner befugt, nach vorgängiger Androhung die Ware öffentlich versteigern zu lassen; er kann, wenn die Ware einen Börsen- oder Marktpreis hat, nach vorgängiger Androhung den Verkauf auch aus freier Hand durch einen zu solchen Verkäufen öffentlich ermächtigten Handelsmakler oder durch eine zur öffentlichen Versteigerung befugte Person zum laufenden Preise bewirken…
(see above)

This bit is not as easy, considering there isn’t really any auction option available outside Germany. A translation provided by the University of Texas describes the procedure as follows:
"…after the buyer’s default to take delivery, he had by auction resold the merchandise and, converting it into French currency…"
https://law.utexas.edu/transnational/foreign-law-translation...

…Ist die Ware dem Verderb ausgesetzt und Gefahr im Verzug, so bedarf es der vorgängigen Androhung nicht; dasselbe gilt, wenn die Androhung aus anderen Gründen untunlich ist.
(see above)

(3) Der Selbsthilfeverkauf erfolgt für Rechnung des säumigen Käufers.

Now those paragraphs, however, can be found in Section 48 of the Sale of Goods Act:
"(3) Where the goods are of a perishable nature, or where the unpaid seller gives notice to the buyer of his intention to re-sell, and the buyer does not within a reasonable time pay or tender the price, the unpaid seller may re-sell the goods and recover from the original buyer damages for any loss occasioned by his breach of contract."
https://www.legislation.gov.uk/ukpga/1979/54/section/48

(4) Der Verkäufer und der Käufer können bei der öffentlichen Versteigerung mitbieten.

See second list item.

(5) Im Falle der öffentlichen Versteigerung hat der Verkäufer den Käufer von der Zeit und dem Orte der Versteigerung vorher zu benachrichtigen; von dem vollzogenen Verkaufe hat er bei jeder Art des Verkaufs dem Käufer unverzüglich Nachricht zu geben. Im Falle der Unterlassung ist er zum Schadensersatz verpflichtet. Die Benachrichtigungen dürfen unterbleiben, wenn sie untunlich sind.

See third list item.

After reading a few excerpts from "Contracts in General, Chapter 16: Remedies for Breach of Contract (Courses of Action Open to a Party Aggrieved)" by G. H. Treitel (2020) and the "International Encyclopedia of Comparative Law" by B. G. Garth (1976), I believe resale to be a safe bet, in line with Section 38 of the Sale of Goods Act:
"Subject to this and any other Act, notwithstanding that the property in the goods may have passed to the buyer, the unpaid seller of goods, as such, has by implication of law—
(a) a lien on the goods or right to retain them for the price while he is in possession of them;
(b) in case of the insolvency of the buyer, a right of stopping the goods in transit after he has parted with the possession of them;
(c) a right of re-sale as limited by this Act."
https://www.legislation.gov.uk/ukpga/1979/54/section/39

To add some global perspective here, I also found this Canadian document from 1929 on the "Seller’s right to resell":
https://www.canlii.org/en/commentary/doc/1929CanLIIDocs65#!f...

In short, you’re going to be understood--as long as you leave out the auction bit, I’d say.

You have several options at your disposal when it comes to the English counterpart of Selbsthilfeverkauf, such as "re-sale on buyer’s default" (p. 88) here…
https://ia600208.us.archive.org/28/items/cu31924022471134/cu...

…or "resale following default by buyer" (thanks to Robin for the idea).

The Selbsthilfeverkauf is even part of the CISG, that is, the United Nations Convention on Contracts for the International Sales of Goods, though they only use "sale":

"(1) A party who is bound to preserve the goods in accordance with article 85 or 86 may sell them by any appropriate means if there has been an unreasonable delay by the other party in taking possession of the goods or in taking them back or in paying the price or the cost of preservation, provided that reasonable notice of the intention to sell has been given to the other party.
(2) If the goods are subject to rapid deterioration or their preservation would involve unreasonable expense, a party who is bound to preserve the goods in accordance with article 85 or 86 must take reasonable measures to sell them. To the extent possible he must give notice to the other party of his intention to sell.
(3) A party selling the goods has the right to retain out of the proceeds of sale an amount equal to the reasonable expenses of preserving the goods and of selling them. He must account to the other party for the balance."
https://cisg-online.org/cisg-article-by-article/part-3/art.-...

They don't mention an auction either; but it certainly wouldn't hurt to include some kind of reference to such an internationally known (and globally used) framework.

In short, I just wouldn't add anything that won't be immediately understood by an international audience (whom these T&Cs are presumably addressed to).