It is not justified, nor is the passage hard to translate:
אִם־י֛וֹם א֥וֹ יוֹמַ֖יִם יַעֲמֹ֑ד
ʾim-yôm ʾô yômayim yaʿămōḏ
if day or [dual-form]days [he] persists
You should not fixate on the sense of "stand" for 'md, as this is a Hebrew idiom that is rarely meant literally -- e.g. to be in a state of standing -- and is usually meant in the sense of "hold on", "persist", "remain", "endure", "abide", "continue", and less frequently "present oneself" (e.g. stand before the Lord).
Proverbs 27:4b (KJV 1900)
But who is able to stand before envy?
Basically the main sense is to not succumb to whatever the contextual challenge is, which in this case means to not die.
If the text would have meant "to stand up" or "arise", then it would have been קום.
When 'md is meant in the physical sense, it is never about accomplishing the act of standing up, but rather to be in a state of standing, to continue in a state of standing (imperfect) or to accomplish the state of standing in the sense of to stop moving - e.g. to stop if there is no direct object and to set someone or something if there is. E.g Nu 5.18 "The Priest shall set the woman before the Lord". There is no verb tense that can make it mean "to stand up" in the physical sense of getting out of a sick bed.
Only in the metaphoric sense can it be translated with an english target as "stand up", and in this case it means "to establish", as in the sense of standing up an army. Similarly with an english target, 'md can be translated into "stand with, stand against, stand in the place of" but all in a metaphorical sense.
But let's go ahead and translate it as "stand". Then still, there is no Hebrew verbal form that can convert "stand day or [dual] days" into "stand after one or two days" or "be healed within one or two days". That interpretation requires doing violence to the text as it inserts a preposition or similar marker not present. E.g. to say "in" two days needs a ב or "at the end of two days" would need a מקץ. Point is, there is no verbal form that can insert those markers for you.
Let's take a look at the ancient translations, starting with the targums, which were the "official" translations into Aramaic, together with explanatory material, that can often be used to clear up the meaning of the hebrew at least as understood by the rabbis. They all use the verb qym, meaning "to survive", because they understand the idiom "to stand" in this case means to not die.
- Neofiti[1]: but if he survives a day or two
- Onqelos[2]: But if he will survive for a day or two days
Now the LXX[4]:
- ἐὰν δὲ διαβιώσῃ ἡμέραν μίαν ἢ δύο (But if he survives one day or two)
Clementine Vulgate[5]:
- Sin autem uno die vel duobus supervixerit [but if he survives a day or two]
The 1985 Jewish Publication Society Tanakh[3]:
- But if he survives a day or two, he is not to be avenged
Lexham English Bible:
- Yet if he survives a day or two days
ESV:
- But if the slave survives a day or two
NRSV (1989):
- But if the slave survives a day or two
NET:
- if the injured servant survives one or two days
KJV:
- Notwithstanding, if he continue a day or two,
Douay-Rheims (based on Vulgate):
- But if the party remain alive a day or two
It's really hard to think of a less difficult passage to translate, or one in which there has historically been more unanimity.
Until very recently -- when a small number of (obscure) translations started to trickle out late in the 20th Century, which apparently found the Hebrew ambiguous or even cryptic. They argued that there was either a missing "after" or a missing "within", and so the text should read "if the slave stands after one or two days" or a slave [literally] stands up within one or two days, and all of a sudden an offensive scripture was made more palatable to modern tastes. But this is not good hermeneutics, and is not justified by the text.
[1] Kevin Cathcart, Michael Maher, and Martin McNamara, eds., The Aramaic Bible: Targum Neofiti 1: Exodus and Targum Pseudo-Jonathan: Exodus, trans. Martin McNamara, Michael Maher, and Robert Hayward, vol. 2 (Collegeville, MN: The Liturgical Press, 1994), Ex 21:21.
[2] Kevin Cathcart, Michael Maher, and Martin McNamara, eds., The Aramaic Bible: The Targum of Onqelos to Exodus, trans. Bernard Grossfeld, vol. 7 (Collegeville, MN: Liturgical Press, 1990), Ex 21:21.
[3] Jewish Publication Society, Tanakh: The Holy Scriptures (Philadelphia: Jewish Publication Society, 1985), Ex 21:21.
[4] Randall Tan and David A. deSilva, Logos Bible Software, The Lexham Greek-English Interlinear Septuagint: Rahlfs Edition (Logos Bible Software, 2009),
[5] Biblia Sacra Juxta Vulgatam Clementinam., Ed. electronica. (Bellingham, WA: Logos Bible Software, 2005), Ex 21:21.