Yes both wget and curl support limiting your download rate. Both options are directly mentioned in the man page.
Specify the maximum transfer rate you want curl to use.
This feature is useful if you have a limited pipe and
you'd like your transfer not to use your entire bandwidth.
The given speed is measured in bytes/second, unless a suffix
is appended. Appending 'k' or 'K' will count the number
as kilobytes, 'm' or M' makes it megabytes, while 'g' or 'G'
makes it gigabytes. Examples: 200K, 3m and 1G.
curl --limit-rate 423K
Limit the download speed to amount bytes per second. Amount may
be expressed in bytes, kilobytes with the k suffix, or
megabytes with the m suffix. For example, --limit-rate=20k will limit
the retrieval rate to 20KB/s. This is useful when, for
whatever reason, you don't want Wget to consume
the entire available bandwidth.