How to make your own check mark with rounded corners for the radio input (input) CSS

It will be easier to assemble it from two composite rounded rectangles + transform: rotate() at suitable angles... I picked up the numbers by eye:

.radio {
  display: none;
}

.pseudo-radio {
  font-size: 100px;
  /* Что прикольно, всё остальное будет регулироваться относительно этого размера */
  
  display: inline-block;
  position: relative;
  
  width: 1em;
  height: 1em;
  
  border: 2px solid #929;
  cursor: pointer;
}

.radio:checked + .pseudo-radio::before,
.radio:checked + .pseudo-radio::after {
  display: block;
}

.pseudo-radio::before,
.pseudo-radio::after {
  content: "";
  position: absolute;
  display: none;
  
  bottom: 0.28em;
  left: 0.05em;
  transform: rotate(40deg);
  
  width: 0.6em;
  height: 0.2em;
  
  background-color: #f80;
  border-radius: 1em;
}
.pseudo-radio::after {  
  bottom: 0.4em;
  left: 0.28em;
  transform: rotate(-60deg);
  
  width: 0.8em;
  height: 0.2em;
}

<label>
  <input type="radio" class="radio" name="bubu" checked>
  <span class="pseudo-radio"></span>
</label>
  
<label>
  <input type="radio" class="radio" name="bubu">
  <span class="pseudo-radio"></span>
</label>

<label>
  <input type="radio" class="radio" name="bubu">
  <span class="pseudo-radio"></span>
</label>

Colors if you touch up something.

/* Customize the label (the container) */
.container {
  display: block;
  position: relative;
  padding-left: 35px;
  margin-bottom: 12px;
  cursor: pointer;
  font-size: 22px;
  -webkit-user-select: none;
  -moz-user-select: none;
  -ms-user-select: none;
  user-select: none;
}

/* Hide the browser's default checkbox */
.container input {
  position: absolute;
  opacity: 0;
  cursor: pointer;
  height: 0;
  width: 0;
}

/* Create a custom checkbox */
.checkmark {
  position: absolute;
  top: 0;
  left: 0;
  border: 1px solid grey;
  border-radius: 5px;
  height: 25px;
  width: 25px;
  background-color: #eee;
}

/* On mouse-over, add a grey background color */
.container:hover input ~ .checkmark {
  background-color: #ccc;
}

/* When the checkbox is checked, add a blue background */
.container input:checked ~ .checkmark {
  background-color: #fff;
}

/* Create the checkmark/indicator (hidden when not checked) */
.checkmark:after {
  content: "";
  position: absolute;
  display: none;
}

/* Show the checkmark when checked */
.container input:checked ~ .checkmark:after {
  display: block;
}

/* Style the checkmark/indicator */
.container .checkmark:after {
  left: 9px;
  top: 5px;
  width: 5px;
  height: 10px;
  border: solid #2196F3;
  border-width: 0 3px 3px 0;
  -webkit-transform: rotate(45deg);
  -ms-transform: rotate(45deg);
  transform: rotate(45deg);
}

<label class="container">INput
  <input type="checkbox">
  <span class="checkmark"></span>
</label>

Option on pure CSS

.input-radio {
  display: inline-block;
}

.input-radio input[type="radio"] {
  display: none;
}

.input-radio .-custom {
  display: block;
  width: 40px;
  height: 40px;
  border: 2px solid #cacaca;
  box-sizing: border-box;
  cursor: pointer;
  position: relative;
}

.input-radio .-custom::before {
  content: '';
  display: block;
  width: calc(100% - 16px);
  height: calc(100% - 16px);
  background: #3c8dbc;
  margin: 8px;
}

.input-radio input[type="radio"]:checked ~ .-custom::before {
  content: '';
  display: block;
  height: 10px;
  background: transparent !important;
  border: 6px solid #3c8dbc;
  border-top: 0;
  border-right: 0;
  margin: 0;
  position: absolute;
  top: 50%;
  left: 50%;
  transform: translate(-50%, -75%) rotate(-45deg);
}

.input-radio .-custom:hover,
.input-radio input[type="radio"]:checked ~ .-custom:hover::before {
  border-color: #0076c3;
}

.input-radio .-custom:hover::before  {
  background: #0076c3;
}

.input-radio.--border-radius .-custom {
  border-radius: 10px;
}

.input-radio.--border-radius-v2 .-custom {
  border-radius: 10px;
}

.input-radio.--border-radius-v2 input[type="radio"]:not(:checked) ~ .-custom::before {
  border-radius: 6px;
}
.input-radio.--circle .-custom,
.input-radio.--circle input[type="radio"]:not(:checked) ~ .-custom::before {
  border-radius: 50%;
}

<label for="input00" class="input-radio">
  <input id="input00" type="radio" name="i0[]">
  <div class="-custom"></div>
</label>

<label for="input01" class="input-radio">
  <input id="input01" type="radio" name="i0[]" checked>
  <div class="-custom"></div>
</label>
<br>
<label for="input10" class="input-radio --border-radius">
  <input id="input10" type="radio" name="i1[]">
  <div class="-custom"></div>
</label>

<label for="input11" class="input-radio --border-radius">
  <input id="input11" type="radio" name="i1[]" checked>
  <div class="-custom"></div>
</label>
<br>
<label for="input20" class="input-radio --border-radius-v2">
  <input id="input20" type="radio" name="i2[]">
  <div class="-custom"></div>
</label>

<label for="input21" class="input-radio --border-radius-v2">
  <input id="input21" type="radio" name="i2[]" checked>
  <div class="-custom"></div>
</label>
<br>
<label for="input30" class="input-radio --circle">
  <input id="input30" type="radio" name="i3[]">
  <div class="-custom"></div>
</label>

<label for="input31" class="input-radio --circle">
  <input id="input31" type="radio" name="i3[]" checked>
  <div class="-custom"></div>
</label>

UPD: For some reason, I did not check for operability then.
The ID was not unique and as a result did not work.