Deleting large files from 'My Downloads"

Running Windows 98 on a Gateway Performace 650.
There are approximately 43 files/programs saved in "My Downloads" with file extensions .exe, .dat, PIF, BI1, etc.. Some are for programs that I know I need and want to keep running on this computer.

Between my older kids and myself, I think they've been been saved when downloading by clicking on 'save to file' instead of 'open file.'

In trying to free up some space and allow the computer to run more efficiently with less strain on it, can these files be deleted without actually deleting the programs used or would this help at all?

When I click to delete, an intimidating warning box appears saying:
"This file is a program. If you delete it, you will no longer be able to run this program or edit some documents. Are you sure you want to send it to the Recycle Bin?"

Some of the files are:
Spybot.exe
SpywareBlaster.exe
flashplayer.exe
AVG.exe
AdbeRdr.exe

There are several games with the .exe extension as well.

Then there are some titled:
IFlash.pif
hypothb07.dat
hypoth.bil1
hypoth.bil2 (etc. up to .bil7)