Using WPF in an ElementHost control - pass data from the c# Control's constructor to the underlying XAML to allow for different instances

Question

Running off a tutorial from CodeProject I've succeeded in adding a WPF item to my Winforms project. My WinformsProject adds a slightly altered version of ElementHost, which contains a xaml object as a child from a separate project (with the alterations to ElementHost seemingly just to pass property and methods between the two projects).

My XAML code is:

<UserControl x:Class="WindowsFormsControlLibrary1.RoundedButtonWithSVG"

            xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
            xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
            xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
            xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:windowsformscontrollibrary1="clr-namespace:WindowsFormsControlLibrary1"
             mc:Ignorable="d" 
             d:DesignHeight="50" d:DesignWidth="250">
    <Grid>
        <Button x:Name="myButton" HorizontalAlignment="Left"  Background="White" Height="50" VerticalAlignment="Top" Width="250" BorderBrush="#FFBFBFBF" Click="myButton_Click">
            <Button.Resources>
                <Style TargetType="Border">
                    <Setter Property="CornerRadius" Value="5"/>
                </Style>
            </Button.Resources>
            
            <Viewbox xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation" Stretch="Uniform">
                <Canvas Name="svg117" Width="32" Height="32" >
                    <!--Unknown tag: sodipodi:namedview-->
                    <Path xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml" Name="path115" Fill="#FF008A9F" StrokeThickness=".4025" Stroke="#FF008A9F">
                        <Path.Data> <!--Below is the SVG for an icon-->
                            <PathGeometry Figures="m31.63 0.27366c-0.12545-0.088189-0.29069-0.098564-0.4267-0.027534l-30.786 16.139c-0.19792 0.10375-0.27291 0.34517-0.16751 0.53991 0.048232 0.08899 0.12898 0.15682 0.22597 0.18955l9.4117 3.2015 0.17011 0.05507 2.6795 8.2814c0.04291 0.13288 0.1533 0.23384 0.2911 0.26696 0.03167 0.0072 0.06411 0.01117 0.09663 0.01117 0.10767 0 0.21091-0.0419 0.28704-0.11692l5.5775-5.4817 8.2128 2.7833c0.11327 0.03911 0.23872 0.02634 0.34144-0.03512 0.10272-0.06066 0.17295-0.16281 0.19203-0.27933l4.0599-25.14c0.02395-0.14964-0.04019-0.29968-0.16564-0.38747zm-30.003 16.381 26.809-14.053c0.0016-0.0012 0.0045-7.981e-4 0.0057 7.981e-4 0.0012 0.0016 8.12e-4 0.00439-8.12e-4 0.00559l-18.205 16.976-8.607-2.9218c-0.00231-7.98e-4 -0.00349-0.0032-0.00268-0.0056 2.842e-4 -7.98e-4 8.12e-4 -0.0016 0.00146-2e-3zm9.2038 3.4745 17.873-16.667c0.0016-0.0016 0.0041-0.0016 0.0057 0 2e-3 0.0012 2e-3 0.00399 4.06e-4 0.00559l-13.97 17.868c-0.0311 0.03871-0.05387 0.0834-0.06699 0.13129l-1.5805 5.6265c0 2e-3 -0.0018 4e-3 -0.0041 4e-3 -0.0022 0-0.0041-2e-3 -0.0041-4e-3zm3.077 7.0571 1.4303-5.0918 2.7969 0.94773-4.2223 4.1481c-0.0022 3.99e-4 -0.0043-7.98e-4 -0.0048-0.0032-4.1e-5 -3.99e-4 -8.1e-5 -3.99e-4 -8.1e-5 -7.98e-4zm13.097-1.9821-11.277-3.8221 14.987-19.168c8.12e-4 -2e-3 0.0028-0.00279 0.0049-2e-3 2e-3 7.981e-4 0.0028 0.00279 2e-3 0.00479l-3.712 22.984c-4.06e-4 2e-3 -0.0024 0.0036-0.0049 0.0032z" FillRule="NonZero"/>
                        </Path.Data>
                    </Path>
                </Canvas>
            </Viewbox>
        </Button>

    </Grid>
</UserControl>

Essentially the above is just a simple button, with rounded corners and an SVG image (which would all make our UI Girl exceedingly happy). Now I need a bunch of these, each with different text and images. My question is, can I somehow override the xaml settings based on fields from the c# constructor? So in this case, can I override the Figures property of the PathGeometry in the Xaml to set whatever image I need for the given button? Something like the following as the .xaml.cs file

public partial class ComboBoxWithGrid : UserControl
{
    public ComboBoxWithGrid(string imageString)
    {
        this.boundImageStringProperty = imageString;
        InitializeComponent();
    }
    public string boundImageStringProperty = ""; //Can I Inject this into the xaml in any way?
    public Action buttonClickEvent;
    private void button_Click(object sender, RoutedEventArgs e)
    {
        buttonClickEvent();
    }
}

Doing the above would let me use the one xaml object for most of my buttons, just with different constructor arguments but I'm afraid I'm not XAML Literate enough to figure any of this out, and most guides I find online detail how to send data from the xaml constructor to the c# base (not the other way around). Is any of this possible?